---
OA_place: repository
OA_type: green
_id: '22026'
abstract:
- lang: eng
  text: We address two pressing questions in the theory of the Korteweg–de Vries (KdV)
    equation. First, we show the uniqueness of solutions to KdV that are merely bounded,
    without any further decay, regularity, periodicity, or almost periodicity assumptions.
    The second question, emphasized by Deift, regards whether almost periodic initial
    data leads to almost periodic solutions to KdV. Building on the new observation
    that this is false for the Airy equation, we construct an example of almost periodic
    initial data whose KdV evolution remains bounded, but fails to be almost periodic
    at a later time. Our uniqueness result ensures that the solution constructed is
    the unique development of this initial data.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Andreia
  full_name: Chapouto, Andreia
  last_name: Chapouto
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: 'Chapouto A, Killip R, Vişan M. Bounded solutions of KdV: Uniqueness and the
    loss of almost periodicity. <i>Duke Mathematical Journal</i>. 2024;173(7):1227-1267.
    doi:<a href="https://doi.org/10.1215/00127094-2023-0035">10.1215/00127094-2023-0035</a>'
  apa: 'Chapouto, A., Killip, R., &#38; Vişan, M. (2024). Bounded solutions of KdV:
    Uniqueness and the loss of almost periodicity. <i>Duke Mathematical Journal</i>.
    Duke University Press. <a href="https://doi.org/10.1215/00127094-2023-0035">https://doi.org/10.1215/00127094-2023-0035</a>'
  chicago: 'Chapouto, Andreia, Rowan Killip, and Monica Vişan. “Bounded Solutions
    of KdV: Uniqueness and the Loss of Almost Periodicity.” <i>Duke Mathematical Journal</i>.
    Duke University Press, 2024. <a href="https://doi.org/10.1215/00127094-2023-0035">https://doi.org/10.1215/00127094-2023-0035</a>.'
  ieee: 'A. Chapouto, R. Killip, and M. Vişan, “Bounded solutions of KdV: Uniqueness
    and the loss of almost periodicity,” <i>Duke Mathematical Journal</i>, vol. 173,
    no. 7. Duke University Press, pp. 1227–1267, 2024.'
  ista: 'Chapouto A, Killip R, Vişan M. 2024. Bounded solutions of KdV: Uniqueness
    and the loss of almost periodicity. Duke Mathematical Journal. 173(7), 1227–1267.'
  mla: 'Chapouto, Andreia, et al. “Bounded Solutions of KdV: Uniqueness and the Loss
    of Almost Periodicity.” <i>Duke Mathematical Journal</i>, vol. 173, no. 7, Duke
    University Press, 2024, pp. 1227–67, doi:<a href="https://doi.org/10.1215/00127094-2023-0035">10.1215/00127094-2023-0035</a>.'
  short: A. Chapouto, R. Killip, M. Vişan, Duke Mathematical Journal 173 (2024) 1227–1267.
das_tickbox: '1'
date_created: 2026-06-19T07:34:05Z
date_published: 2024-05-15T00:00:00Z
date_updated: 2026-06-22T10:32:25Z
day: '15'
doi: 10.1215/00127094-2023-0035
extern: '1'
external_id:
  arxiv:
  - '2209.07501'
intvolume: '       173'
issue: '7'
keyword:
- Almost-periodic solutions
- Korteweg–de Vries
- unconditional uniqueness
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2209.07501
month: '05'
oa: 1
oa_version: Preprint
page: 1227-1267
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Bounded solutions of KdV: Uniqueness and the loss of almost periodicity'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 173
year: '2024'
...
---
_id: '179'
abstract:
- lang: eng
  text: An asymptotic formula is established for the number of rational points of
    bounded anticanonical height which lie on a certain Zariski dense subset of the
    biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified
    Manin conjecture for this variety, in which the removal of a thin set of rational
    points is allowed.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
- first_name: Roger
  full_name: Heath Brown, Roger
  last_name: Heath Brown
citation:
  ama: Browning TD, Heath Brown R. Density of rational points on a quadric bundle
    in ℙ3×ℙ3. <i>Duke Mathematical Journal</i>. 2020;169(16):3099-3165. doi:<a href="https://doi.org/10.1215/00127094-2020-0031">10.1215/00127094-2020-0031</a>
  apa: Browning, T. D., &#38; Heath Brown, R. (2020). Density of rational points on
    a quadric bundle in ℙ3×ℙ3. <i>Duke Mathematical Journal</i>. Duke University Press.
    <a href="https://doi.org/10.1215/00127094-2020-0031">https://doi.org/10.1215/00127094-2020-0031</a>
  chicago: Browning, Timothy D, and Roger Heath Brown. “Density of Rational Points
    on a Quadric Bundle in ℙ3×ℙ3.” <i>Duke Mathematical Journal</i>. Duke University
    Press, 2020. <a href="https://doi.org/10.1215/00127094-2020-0031">https://doi.org/10.1215/00127094-2020-0031</a>.
  ieee: T. D. Browning and R. Heath Brown, “Density of rational points on a quadric
    bundle in ℙ3×ℙ3,” <i>Duke Mathematical Journal</i>, vol. 169, no. 16. Duke University
    Press, pp. 3099–3165, 2020.
  ista: Browning TD, Heath Brown R. 2020. Density of rational points on a quadric
    bundle in ℙ3×ℙ3. Duke Mathematical Journal. 169(16), 3099–3165.
  mla: Browning, Timothy D., and Roger Heath Brown. “Density of Rational Points on
    a Quadric Bundle in ℙ3×ℙ3.” <i>Duke Mathematical Journal</i>, vol. 169, no. 16,
    Duke University Press, 2020, pp. 3099–165, doi:<a href="https://doi.org/10.1215/00127094-2020-0031">10.1215/00127094-2020-0031</a>.
  short: T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165.
das_tickbox: '0'
date_created: 2018-12-11T11:45:02Z
date_published: 2020-09-10T00:00:00Z
date_updated: 2026-08-06T11:22:52Z
day: '10'
department:
- _id: TiBr
doi: 10.1215/00127094-2020-0031
external_id:
  arxiv:
  - '1805.10715'
  isi:
  - '000582676300002'
intvolume: '       169'
isi: 1
issue: '16'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1805.10715
month: '09'
oa: 1
oa_version: Preprint
page: 3099-3165
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Density of rational points on a quadric bundle in ℙ3×ℙ3
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 169
year: '2020'
...
---
_id: '8423'
abstract:
- lang: eng
  text: In this paper we show that for a generic strictly convex domain, one can recover
    the eigendata corresponding to Aubry–Mather periodic orbits of the induced billiard
    map from the (maximal) marked length spectrum of the domain.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guan
  full_name: Huang, Guan
  last_name: Huang
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: Alfonso
  full_name: Sorrentino, Alfonso
  last_name: Sorrentino
citation:
  ama: Huang G, Kaloshin V, Sorrentino A. On the marked length spectrum of generic
    strictly convex billiard tables. <i>Duke Mathematical Journal</i>. 2017;167(1):175-209.
    doi:<a href="https://doi.org/10.1215/00127094-2017-0038">10.1215/00127094-2017-0038</a>
  apa: Huang, G., Kaloshin, V., &#38; Sorrentino, A. (2017). On the marked length
    spectrum of generic strictly convex billiard tables. <i>Duke Mathematical Journal</i>.
    Duke University Press. <a href="https://doi.org/10.1215/00127094-2017-0038">https://doi.org/10.1215/00127094-2017-0038</a>
  chicago: Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “On the Marked Length
    Spectrum of Generic Strictly Convex Billiard Tables.” <i>Duke Mathematical Journal</i>.
    Duke University Press, 2017. <a href="https://doi.org/10.1215/00127094-2017-0038">https://doi.org/10.1215/00127094-2017-0038</a>.
  ieee: G. Huang, V. Kaloshin, and A. Sorrentino, “On the marked length spectrum of
    generic strictly convex billiard tables,” <i>Duke Mathematical Journal</i>, vol.
    167, no. 1. Duke University Press, pp. 175–209, 2017.
  ista: Huang G, Kaloshin V, Sorrentino A. 2017. On the marked length spectrum of
    generic strictly convex billiard tables. Duke Mathematical Journal. 167(1), 175–209.
  mla: Huang, Guan, et al. “On the Marked Length Spectrum of Generic Strictly Convex
    Billiard Tables.” <i>Duke Mathematical Journal</i>, vol. 167, no. 1, Duke University
    Press, 2017, pp. 175–209, doi:<a href="https://doi.org/10.1215/00127094-2017-0038">10.1215/00127094-2017-0038</a>.
  short: G. Huang, V. Kaloshin, A. Sorrentino, Duke Mathematical Journal 167 (2017)
    175–209.
date_created: 2020-09-17T10:42:42Z
date_published: 2017-12-08T00:00:00Z
date_updated: 2021-01-12T08:19:11Z
day: '08'
doi: 10.1215/00127094-2017-0038
extern: '1'
external_id:
  arxiv:
  - '1603.08838'
intvolume: '       167'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1603.08838
month: '12'
oa: 1
oa_version: Preprint
page: 175-209
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
status: public
title: On the marked length spectrum of generic strictly convex billiard tables
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 167
year: '2017'
...
---
_id: '8505'
abstract:
- lang: eng
  text: The classical principle of least action says that orbits of mechanical systems
    extremize action; an important subclass are those orbits that minimize action.
    In this paper we utilize this principle along with Aubry-Mather theory to construct
    (Birkhoff) regions of instability for a certain three-body problem, given by a
    Hamiltonian system of 2 degrees of freedom. We believe that these methods can
    be applied to construct instability regions for a variety of Hamiltonian systems
    with 2 degrees of freedom. The Hamiltonian model we consider describes dynamics
    of a Sun-Jupiter-comet system, and under some simplifying assumptions, we show
    the existence of instabilities for the orbit of the comet. In particular, we show
    that a comet which starts close to an orbit in the shape of an ellipse of eccentricity
    e=0.66 can increase in eccentricity up to e=0.96. In the sequels to this paper,
    we extend the result to beyond e=1 and show the existence of ejection orbits.
    Such orbits are initially well within the range of our solar system. This might
    give an indication of why most objects rotating around the Sun in our solar system
    have relatively low eccentricity.
article_processing_charge: No
article_type: original
author:
- first_name: Joseph
  full_name: Galante, Joseph
  last_name: Galante
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
citation:
  ama: Galante J, Kaloshin V. Destruction of invariant curves in the restricted circular
    planar three-body problem by using comparison of action. <i>Duke Mathematical
    Journal</i>. 2011;159(2):275-327. doi:<a href="https://doi.org/10.1215/00127094-1415878">10.1215/00127094-1415878</a>
  apa: Galante, J., &#38; Kaloshin, V. (2011). Destruction of invariant curves in
    the restricted circular planar three-body problem by using comparison of action.
    <i>Duke Mathematical Journal</i>. Duke University Press. <a href="https://doi.org/10.1215/00127094-1415878">https://doi.org/10.1215/00127094-1415878</a>
  chicago: Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in
    the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.”
    <i>Duke Mathematical Journal</i>. Duke University Press, 2011. <a href="https://doi.org/10.1215/00127094-1415878">https://doi.org/10.1215/00127094-1415878</a>.
  ieee: J. Galante and V. Kaloshin, “Destruction of invariant curves in the restricted
    circular planar three-body problem by using comparison of action,” <i>Duke Mathematical
    Journal</i>, vol. 159, no. 2. Duke University Press, pp. 275–327, 2011.
  ista: Galante J, Kaloshin V. 2011. Destruction of invariant curves in the restricted
    circular planar three-body problem by using comparison of action. Duke Mathematical
    Journal. 159(2), 275–327.
  mla: Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the
    Restricted Circular Planar Three-Body Problem by Using Comparison of Action.”
    <i>Duke Mathematical Journal</i>, vol. 159, no. 2, Duke University Press, 2011,
    pp. 275–327, doi:<a href="https://doi.org/10.1215/00127094-1415878">10.1215/00127094-1415878</a>.
  short: J. Galante, V. Kaloshin, Duke Mathematical Journal 159 (2011) 275–327.
date_created: 2020-09-18T10:47:41Z
date_published: 2011-08-04T00:00:00Z
date_updated: 2021-01-12T08:19:45Z
day: '04'
doi: 10.1215/00127094-1415878
extern: '1'
intvolume: '       159'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '08'
oa_version: None
page: 275-327
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
status: public
title: Destruction of invariant curves in the restricted circular planar three-body
  problem by using comparison of action
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 159
year: '2011'
...
---
OA_place: repository
OA_type: green
_id: '22039'
abstract:
- lang: eng
  text: "We establish global well-posedness and scattering for solutions to the defocusing\r\nmass-critical
    (pseudoconformal) nonlinear Schrodinger equation ¨ iut +\x01u =|u|4/nu\r\nfor
    large, spherically symmetric, L^2x (Rn) initial data in dimensions n ≥ 3. After
    using\r\nthe concentration-compactness reductions in [32] to reduce to eliminating
    blow-up\r\nsolutions that are almost periodic modulo scaling, we obtain a frequency-localized\r\nMorawetz
    estimate and exclude a mass evacuation scenario (somewhat analogously\r\nto [10],
    [23], [36]) in order to conclude the argument"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Terence
  full_name: Tao, Terence
  last_name: Tao
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
- first_name: Xiaoyi
  full_name: Zhang, Xiaoyi
  last_name: Zhang
citation:
  ama: Tao T, Vişan M, Zhang X. Global well-posedness and scattering for the defocusing
    mass-critical nonlinear Schrödinger equation for radial data in high dimensions.
    <i>Duke Mathematical Journal</i>. 2007;140(1):165-202. doi:<a href="https://doi.org/10.1215/s0012-7094-07-14015-8">10.1215/s0012-7094-07-14015-8</a>
  apa: Tao, T., Vişan, M., &#38; Zhang, X. (2007). Global well-posedness and scattering
    for the defocusing mass-critical nonlinear Schrödinger equation for radial data
    in high dimensions. <i>Duke Mathematical Journal</i>. Duke University Press. <a
    href="https://doi.org/10.1215/s0012-7094-07-14015-8">https://doi.org/10.1215/s0012-7094-07-14015-8</a>
  chicago: Tao, Terence, Monica Vişan, and Xiaoyi Zhang. “Global Well-Posedness and
    Scattering for the Defocusing Mass-Critical Nonlinear Schrödinger Equation for
    Radial Data in High Dimensions.” <i>Duke Mathematical Journal</i>. Duke University
    Press, 2007. <a href="https://doi.org/10.1215/s0012-7094-07-14015-8">https://doi.org/10.1215/s0012-7094-07-14015-8</a>.
  ieee: T. Tao, M. Vişan, and X. Zhang, “Global well-posedness and scattering for
    the defocusing mass-critical nonlinear Schrödinger equation for radial data in
    high dimensions,” <i>Duke Mathematical Journal</i>, vol. 140, no. 1. Duke University
    Press, pp. 165–202, 2007.
  ista: Tao T, Vişan M, Zhang X. 2007. Global well-posedness and scattering for the
    defocusing mass-critical nonlinear Schrödinger equation for radial data in high
    dimensions. Duke Mathematical Journal. 140(1), 165–202.
  mla: Tao, Terence, et al. “Global Well-Posedness and Scattering for the Defocusing
    Mass-Critical Nonlinear Schrödinger Equation for Radial Data in High Dimensions.”
    <i>Duke Mathematical Journal</i>, vol. 140, no. 1, Duke University Press, 2007,
    pp. 165–202, doi:<a href="https://doi.org/10.1215/s0012-7094-07-14015-8">10.1215/s0012-7094-07-14015-8</a>.
  short: T. Tao, M. Vişan, X. Zhang, Duke Mathematical Journal 140 (2007) 165–202.
das_tickbox: '1'
date_created: 2026-06-19T07:45:11Z
date_published: 2007-10-01T00:00:00Z
date_updated: 2026-06-22T13:13:39Z
day: '01'
doi: 10.1215/s0012-7094-07-14015-8
extern: '1'
external_id:
  arxiv:
  - math/0609692
intvolume: '       140'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.math/0609692
month: '10'
oa: 1
oa_version: Preprint
page: 165-202
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global well-posedness and scattering for the defocusing mass-critical nonlinear
  Schrödinger equation for radial data in high dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 140
year: '2007'
...
---
OA_place: repository
OA_type: green
_id: '22050'
abstract:
- lang: eng
  text: "We obtain global well-posedness, scattering, and global L2(n+2)/(n−2)/t,x
    space-time\r\nbounds for energy-space solutions to the energy-critical nonlinear
    Schrodinger (NLS) ¨\r\nequation in Rt × Rn/x , n ≥ 5."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Vişan M. The defocusing energy-critical nonlinear Schrödinger equation in higher
    dimensions. <i>Duke Mathematical Journal</i>. 2007;138(2):281-374. doi:<a href="https://doi.org/10.1215/s0012-7094-07-13825-0">10.1215/s0012-7094-07-13825-0</a>
  apa: Vişan, M. (2007). The defocusing energy-critical nonlinear Schrödinger equation
    in higher dimensions. <i>Duke Mathematical Journal</i>. Duke University Press.
    <a href="https://doi.org/10.1215/s0012-7094-07-13825-0">https://doi.org/10.1215/s0012-7094-07-13825-0</a>
  chicago: Vişan, Monica. “The Defocusing Energy-Critical Nonlinear Schrödinger Equation
    in Higher Dimensions.” <i>Duke Mathematical Journal</i>. Duke University Press,
    2007. <a href="https://doi.org/10.1215/s0012-7094-07-13825-0">https://doi.org/10.1215/s0012-7094-07-13825-0</a>.
  ieee: M. Vişan, “The defocusing energy-critical nonlinear Schrödinger equation in
    higher dimensions,” <i>Duke Mathematical Journal</i>, vol. 138, no. 2. Duke University
    Press, pp. 281–374, 2007.
  ista: Vişan M. 2007. The defocusing energy-critical nonlinear Schrödinger equation
    in higher dimensions. Duke Mathematical Journal. 138(2), 281–374.
  mla: Vişan, Monica. “The Defocusing Energy-Critical Nonlinear Schrödinger Equation
    in Higher Dimensions.” <i>Duke Mathematical Journal</i>, vol. 138, no. 2, Duke
    University Press, 2007, pp. 281–374, doi:<a href="https://doi.org/10.1215/s0012-7094-07-13825-0">10.1215/s0012-7094-07-13825-0</a>.
  short: M. Vişan, Duke Mathematical Journal 138 (2007) 281–374.
das_tickbox: '1'
date_created: 2026-06-19T07:53:37Z
date_published: 2007-06-01T00:00:00Z
date_updated: 2026-06-25T08:18:44Z
day: '01'
doi: 10.1215/s0012-7094-07-13825-0
extern: '1'
external_id:
  arxiv:
  - math/0508298
intvolume: '       138'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.math/0508298
mathsc:
- 35Q55
month: '06'
oa: 1
oa_version: Preprint
page: 281-374
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 138
year: '2007'
...
---
_id: '2730'
abstract:
- lang: eng
  text: We give the leading order semiclassical asymptotics for the sum of the negative
    eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous
    magnetic field. This result can be used to prove that the magnetic Thomas-Fermi
    theory gives the leading order ground state energy of large atoms. We develop
    a new localization scheme well suited to the anisotropic character of the strong
    magnetic field. We also use the basic Lieb-Thirring estimate obtained earlier
    (1996). (orig.) 19 refs.
acknowledgement: The first author gratefully acknowledges financial support from the
  Eidgen6ssiche Technische Hochschule, Forschungsinstitut für Mathematik, Zürich,
  where this work was started. He is also grateful for the hospitality and support
  of Aarhus University during his visits there.
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: 'Erdös L, Solovej J. Semiclassical eigenvalue estimates for the Pauli operator
    with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type
    estimate. <i>Duke Mathematical Journal</i>. 1999;96(1):127-173. doi:<a href="https://doi.org/10.1215/S0012-7094-99-09604-7">10.1215/S0012-7094-99-09604-7</a>'
  apa: 'Erdös, L., &#38; Solovej, J. (1999). Semiclassical eigenvalue estimates for
    the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic
    Lieb-Thirring-type estimate. <i>Duke Mathematical Journal</i>. Duke University
    Press. <a href="https://doi.org/10.1215/S0012-7094-99-09604-7">https://doi.org/10.1215/S0012-7094-99-09604-7</a>'
  chicago: 'Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for
    the Pauli Operator with Strong Nonhomogeneous Magnetic Fields, I: Nonasymptotic
    Lieb-Thirring-Type Estimate.” <i>Duke Mathematical Journal</i>. Duke University
    Press, 1999. <a href="https://doi.org/10.1215/S0012-7094-99-09604-7">https://doi.org/10.1215/S0012-7094-99-09604-7</a>.'
  ieee: 'L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli
    operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type
    estimate,” <i>Duke Mathematical Journal</i>, vol. 96, no. 1. Duke University Press,
    pp. 127–173, 1999.'
  ista: 'Erdös L, Solovej J. 1999. Semiclassical eigenvalue estimates for the Pauli
    operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type
    estimate. Duke Mathematical Journal. 96(1), 127–173.'
  mla: 'Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the
    Pauli Operator with Strong Nonhomogeneous Magnetic Fields, I: Nonasymptotic Lieb-Thirring-Type
    Estimate.” <i>Duke Mathematical Journal</i>, vol. 96, no. 1, Duke University Press,
    1999, pp. 127–73, doi:<a href="https://doi.org/10.1215/S0012-7094-99-09604-7">10.1215/S0012-7094-99-09604-7</a>.'
  short: L. Erdös, J. Solovej, Duke Mathematical Journal 96 (1999) 127–173.
corr_author: '1'
date_created: 2018-12-11T11:59:18Z
date_published: 1999-01-15T00:00:00Z
date_updated: 2024-10-09T20:53:53Z
day: '15'
doi: 10.1215/S0012-7094-99-09604-7
extern: '1'
intvolume: '        96'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 127 - 173
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
publist_id: '4162'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous
  magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 96
year: '1999'
...
---
_id: '2713'
acknowledgement: Work supported by the NSF grant PHY90-19433 A02 and by the Alfred
  Sloan Foundation dissertation fellowship.
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: Erdös L. Estimates on stochastic oscillatory integrals and on the heat kernel
    of the magnetic Schrödinger operator. <i>Duke Mathematical Journal</i>. 1994;76(2):541-566.
    doi:<a href="https://doi.org/10.1215/S0012-7094-94-07619-9">10.1215/S0012-7094-94-07619-9</a>
  apa: Erdös, L. (1994). Estimates on stochastic oscillatory integrals and on the
    heat kernel of the magnetic Schrödinger operator. <i>Duke Mathematical Journal</i>.
    Duke University Press. <a href="https://doi.org/10.1215/S0012-7094-94-07619-9">https://doi.org/10.1215/S0012-7094-94-07619-9</a>
  chicago: Erdös, László. “Estimates on Stochastic Oscillatory Integrals and on the
    Heat Kernel of the Magnetic Schrödinger Operator.” <i>Duke Mathematical Journal</i>.
    Duke University Press, 1994. <a href="https://doi.org/10.1215/S0012-7094-94-07619-9">https://doi.org/10.1215/S0012-7094-94-07619-9</a>.
  ieee: L. Erdös, “Estimates on stochastic oscillatory integrals and on the heat kernel
    of the magnetic Schrödinger operator,” <i>Duke Mathematical Journal</i>, vol.
    76, no. 2. Duke University Press, pp. 541–566, 1994.
  ista: Erdös L. 1994. Estimates on stochastic oscillatory integrals and on the heat
    kernel of the magnetic Schrödinger operator. Duke Mathematical Journal. 76(2),
    541–566.
  mla: Erdös, László. “Estimates on Stochastic Oscillatory Integrals and on the Heat
    Kernel of the Magnetic Schrödinger Operator.” <i>Duke Mathematical Journal</i>,
    vol. 76, no. 2, Duke University Press, 1994, pp. 541–66, doi:<a href="https://doi.org/10.1215/S0012-7094-94-07619-9">10.1215/S0012-7094-94-07619-9</a>.
  short: L. Erdös, Duke Mathematical Journal 76 (1994) 541–566.
date_created: 2018-12-11T11:59:13Z
date_published: 1994-11-01T00:00:00Z
date_updated: 2022-06-03T11:59:06Z
day: '01'
doi: 10.1215/S0012-7094-94-07619-9
extern: '1'
intvolume: '        76'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://projecteuclid.org/journals/duke-mathematical-journal/volume-76/issue-2/Estimates-on-stochastic-oscillatory-integrals-and-on-the-heat-kernel/10.1215/S0012-7094-94-07619-9.short
month: '11'
oa_version: None
page: 541 - 566
publication: Duke Mathematical Journal
publication_identifier:
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
publist_id: '4183'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Estimates on stochastic oscillatory integrals and on the heat kernel of the
  magnetic Schrödinger operator
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 76
year: '1994'
...