---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '19642'
abstract:
- lang: eng
text: We study the criticality and subcriticality of powers (−Δ) α with α>0 of
the discrete Laplacian −Δ acting on ℓ 2 (N). We prove that these positive powers
of the Laplacian are critical if and only if α≥3/2. We complement our analysis
with Hardy-type inequalities for (−Δ) α in the subcritical regimes α∈(0,3/2).
As an illustration of the critical case α≥3/2, we analyze asymptotic properties
of discrete eigenvalues emerging by coupling (−Δ) α with a localized potential.
acknowledgement: "We are grateful to Petr Siegl for a helpful suggestion leading to
Hardy weights with the expected optimal decay rate.\r\nThe authors acknowledge the
support of the EXPRO grant no. 20-17749X of the Czech Science Foundation.\r\n"
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Borbála M
full_name: Gerhát, Borbála M
id: 00ffceaa-f31d-11ee-93bd-f7e13e61af5e
last_name: Gerhát
- first_name: David
full_name: Krejčiřík, David
last_name: Krejčiřík
- first_name: František
full_name: Štampach, František
last_name: Štampach
citation:
ama: Gerhát BM, Krejčiřík D, Štampach F. Criticality transition for positive powers
of the discrete Laplacian on the half line. Revista Matematica Iberoamericana.
2025;41(3):1173-1200. doi:10.4171/RMI/1523
apa: Gerhát, B. M., Krejčiřík, D., & Štampach, F. (2025). Criticality transition
for positive powers of the discrete Laplacian on the half line. Revista Matematica
Iberoamericana. EMS Press. https://doi.org/10.4171/RMI/1523
chicago: Gerhát, Borbála M, David Krejčiřík, and František Štampach. “Criticality
Transition for Positive Powers of the Discrete Laplacian on the Half Line.” Revista
Matematica Iberoamericana. EMS Press, 2025. https://doi.org/10.4171/RMI/1523.
ieee: B. M. Gerhát, D. Krejčiřík, and F. Štampach, “Criticality transition for positive
powers of the discrete Laplacian on the half line,” Revista Matematica Iberoamericana,
vol. 41, no. 3. EMS Press, pp. 1173–1200, 2025.
ista: Gerhát BM, Krejčiřík D, Štampach F. 2025. Criticality transition for positive
powers of the discrete Laplacian on the half line. Revista Matematica Iberoamericana.
41(3), 1173–1200.
mla: Gerhát, Borbála M., et al. “Criticality Transition for Positive Powers of the
Discrete Laplacian on the Half Line.” Revista Matematica Iberoamericana,
vol. 41, no. 3, EMS Press, 2025, pp. 1173–200, doi:10.4171/RMI/1523.
short: B.M. Gerhát, D. Krejčiřík, F. Štampach, Revista Matematica Iberoamericana
41 (2025) 1173–1200.
corr_author: '1'
date_created: 2025-05-04T22:02:32Z
date_published: 2025-01-23T00:00:00Z
date_updated: 2025-09-30T12:23:41Z
day: '23'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.4171/RMI/1523
external_id:
arxiv:
- '2307.09919'
isi:
- '001476507600013'
file:
- access_level: open_access
checksum: 90031b93459af54a6e63ddf2818c6f42
content_type: application/pdf
creator: dernst
date_created: 2025-05-05T11:38:34Z
date_updated: 2025-05-05T11:38:34Z
file_id: '19656'
file_name: 2025_RevistaMat_Gerhat.pdf
file_size: 555474
relation: main_file
success: 1
file_date_updated: 2025-05-05T11:38:34Z
has_accepted_license: '1'
intvolume: ' 41'
isi: 1
issue: '3'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 1173-1200
publication: Revista Matematica Iberoamericana
publication_identifier:
eissn:
- 2235-0616
issn:
- 0213-2230
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Criticality transition for positive powers of the discrete Laplacian on the
half line
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 41
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22077'
abstract:
- lang: eng
text: We prove inverse Strichartz theorems at L^2 regularity for a family of Schrödinger
evolutions in one space dimension. Prior results rely on spacetime Fourier analysis
and are limited to the translation-invariant equation i∂ t u=−1/2 Δu. Motivated
by applications to the mass-critical Schrödinger equation with external potentials
(such as the harmonic oscillator), we use a physical space approach.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Casey
full_name: Jao, Casey
last_name: Jao
- 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: Jao C, Killip R, Vişan M. Mass-critical inverse Strichartz theorems for 1d
Schrödinger operators. Revista Matemática Iberoamericana. 2019;35(3):703-730.
doi:10.4171/rmi/1067
apa: Jao, C., Killip, R., & Vişan, M. (2019). Mass-critical inverse Strichartz
theorems for 1d Schrödinger operators. Revista Matemática Iberoamericana.
European Mathematical Society Press. https://doi.org/10.4171/rmi/1067
chicago: Jao, Casey, Rowan Killip, and Monica Vişan. “Mass-Critical Inverse Strichartz
Theorems for 1d Schrödinger Operators.” Revista Matemática Iberoamericana.
European Mathematical Society Press, 2019. https://doi.org/10.4171/rmi/1067.
ieee: C. Jao, R. Killip, and M. Vişan, “Mass-critical inverse Strichartz theorems
for 1d Schrödinger operators,” Revista Matemática Iberoamericana, vol.
35, no. 3. European Mathematical Society Press, pp. 703–730, 2019.
ista: Jao C, Killip R, Vişan M. 2019. Mass-critical inverse Strichartz theorems
for 1d Schrödinger operators. Revista Matemática Iberoamericana. 35(3), 703–730.
mla: Jao, Casey, et al. “Mass-Critical Inverse Strichartz Theorems for 1d Schrödinger
Operators.” Revista Matemática Iberoamericana, vol. 35, no. 3, European
Mathematical Society Press, 2019, pp. 703–30, doi:10.4171/rmi/1067.
short: C. Jao, R. Killip, M. Vişan, Revista Matemática Iberoamericana 35 (2019)
703–730.
das_tickbox: '1'
date_created: 2026-06-19T08:25:23Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2026-06-30T11:32:27Z
day: '01'
doi: 10.4171/rmi/1067
extern: '1'
external_id:
arxiv:
- '1509.03592'
intvolume: ' 35'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1509.03592
month: '03'
oa: 1
oa_version: Preprint
page: 703-730
publication: Revista Matemática Iberoamericana
publication_identifier:
eissn:
- 2235-0616
issn:
- 0213-2230
publication_status: published
publisher: European Mathematical Society Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mass-critical inverse Strichartz theorems for 1d Schrödinger operators
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2019'
...