---
OA_place: repository
OA_type: green
_id: '22027'
abstract:
- lang: eng
  text: We demonstrate that in three space dimensions, the scattering behaviour of
    semilinear wave equations with quintic-type nonlinearities uniquely determines
    the nonlinearity. The nonlinearity is permitted to depend on both space and time.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicholas
  full_name: Hu, Nicholas
  last_name: Hu
- 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: Hu N, Killip R, Vişan M. Deconvolutional determination of the nonlinearity
    in a semilinear wave equation. <i>Pure and Applied Analysis</i>. 2025;7(1):1-17.
    doi:<a href="https://doi.org/10.2140/paa.2025.7.1">10.2140/paa.2025.7.1</a>
  apa: Hu, N., Killip, R., &#38; Vişan, M. (2025). Deconvolutional determination of
    the nonlinearity in a semilinear wave equation. <i>Pure and Applied Analysis</i>.
    Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/paa.2025.7.1">https://doi.org/10.2140/paa.2025.7.1</a>
  chicago: Hu, Nicholas, Rowan Killip, and Monica Vişan. “Deconvolutional Determination
    of the Nonlinearity in a Semilinear Wave Equation.” <i>Pure and Applied Analysis</i>.
    Mathematical Sciences Publishers, 2025. <a href="https://doi.org/10.2140/paa.2025.7.1">https://doi.org/10.2140/paa.2025.7.1</a>.
  ieee: N. Hu, R. Killip, and M. Vişan, “Deconvolutional determination of the nonlinearity
    in a semilinear wave equation,” <i>Pure and Applied Analysis</i>, vol. 7, no.
    1. Mathematical Sciences Publishers, pp. 1–17, 2025.
  ista: Hu N, Killip R, Vişan M. 2025. Deconvolutional determination of the nonlinearity
    in a semilinear wave equation. Pure and Applied Analysis. 7(1), 1–17.
  mla: Hu, Nicholas, et al. “Deconvolutional Determination of the Nonlinearity in
    a Semilinear Wave Equation.” <i>Pure and Applied Analysis</i>, vol. 7, no. 1,
    Mathematical Sciences Publishers, 2025, pp. 1–17, doi:<a href="https://doi.org/10.2140/paa.2025.7.1">10.2140/paa.2025.7.1</a>.
  short: N. Hu, R. Killip, M. Vişan, Pure and Applied Analysis 7 (2025) 1–17.
date_created: 2026-06-19T07:36:00Z
date_published: 2025-01-22T00:00:00Z
date_updated: 2026-06-24T13:24:38Z
day: '22'
doi: 10.2140/paa.2025.7.1
extern: '1'
external_id:
  arxiv:
  - '2307.00829'
intvolume: '         7'
issue: '1'
keyword:
- dispersive equations
- nonlinear wave equation
- semilinear wave equation
- scattering
- inverse scattering
- deconvolution
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2307.00829
mathsc:
- 35L70
- 35P25
- 35R30
month: '01'
oa: 1
oa_version: Preprint
page: 1-17
publication: Pure and Applied Analysis
publication_identifier:
  eissn:
  - 2578-5885
  issn:
  - 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Deconvolutional determination of the nonlinearity in a semilinear wave equation
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22042'
abstract:
- lang: eng
  text: "We study the L p-theory for the Schrödinger operatorLa with inverse-square
    potential\r\na|x|^−2. Our main result describes when L p-based Sobolev spaces
    defined in terms of the\r\noperator (La)^s/2 agree with those defined via (−\x02)^s/2.We
    consider all regularities 0 < s < 2.\r\nIn order to make the paper self-contained,
    we also review (with proofs) multiplier theorems,\r\nLittlewood–Paley theory,
    and Hardy-type inequalities associated to the operator La."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: R.
  full_name: Killip, R.
  last_name: Killip
- first_name: C.
  full_name: Miao, C.
  last_name: Miao
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
- first_name: J.
  full_name: Zhang, J.
  last_name: Zhang
- first_name: J.
  full_name: Zheng, J.
  last_name: Zheng
citation:
  ama: Killip R, Miao C, Vişan M, Zhang J, Zheng J. Sobolev spaces adapted to the
    Schrödinger operator with inverse-square potential. <i>Mathematische Zeitschrift</i>.
    2018;288(3-4):1273-1298. doi:<a href="https://doi.org/10.1007/s00209-017-1934-8">10.1007/s00209-017-1934-8</a>
  apa: Killip, R., Miao, C., Vişan, M., Zhang, J., &#38; Zheng, J. (2018). Sobolev
    spaces adapted to the Schrödinger operator with inverse-square potential. <i>Mathematische
    Zeitschrift</i>. Springer Nature. <a href="https://doi.org/10.1007/s00209-017-1934-8">https://doi.org/10.1007/s00209-017-1934-8</a>
  chicago: Killip, R., C. Miao, Monica Vişan, J. Zhang, and J. Zheng. “Sobolev Spaces
    Adapted to the Schrödinger Operator with Inverse-Square Potential.” <i>Mathematische
    Zeitschrift</i>. Springer Nature, 2018. <a href="https://doi.org/10.1007/s00209-017-1934-8">https://doi.org/10.1007/s00209-017-1934-8</a>.
  ieee: R. Killip, C. Miao, M. Vişan, J. Zhang, and J. Zheng, “Sobolev spaces adapted
    to the Schrödinger operator with inverse-square potential,” <i>Mathematische Zeitschrift</i>,
    vol. 288, no. 3–4. Springer Nature, pp. 1273–1298, 2018.
  ista: Killip R, Miao C, Vişan M, Zhang J, Zheng J. 2018. Sobolev spaces adapted
    to the Schrödinger operator with inverse-square potential. Mathematische Zeitschrift.
    288(3–4), 1273–1298.
  mla: Killip, R., et al. “Sobolev Spaces Adapted to the Schrödinger Operator with
    Inverse-Square Potential.” <i>Mathematische Zeitschrift</i>, vol. 288, no. 3–4,
    Springer Nature, 2018, pp. 1273–98, doi:<a href="https://doi.org/10.1007/s00209-017-1934-8">10.1007/s00209-017-1934-8</a>.
  short: R. Killip, C. Miao, M. Vişan, J. Zhang, J. Zheng, Mathematische Zeitschrift
    288 (2018) 1273–1298.
date_created: 2026-06-19T07:46:14Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2026-06-25T07:36:26Z
day: '01'
doi: 10.1007/s00209-017-1934-8
extern: '1'
external_id:
  arxiv:
  - '1503.02716'
intvolume: '       288'
issue: 3-4
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1503.02716
mathsc:
- 35P25
- 35Q55
month: '04'
oa: 1
oa_version: Preprint
page: 1273-1298
publication: Mathematische Zeitschrift
publication_identifier:
  eissn:
  - 1432-1823
  issn:
  - 0025-5874
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sobolev spaces adapted to the Schrödinger operator with inverse-square potential
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 288
year: '2018'
...