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Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line. / Коротяев, Евгений Леонидович; Mantile, Andrea; Mokeev, Dmitrii.

In: SIAM Journal on Mathematical Analysis, Vol. 56, No. 2, 2, 05.03.2024, p. 2115-2148.

Research output: Contribution to journal › Article › peer-review

Harvard

Коротяев, ЕЛ, Mantile, A & Mokeev, D 2024, 'Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line', SIAM Journal on Mathematical Analysis, vol. 56, no. 2, 2, pp. 2115-2148. https://doi.org/10.1137/23m1591104

APA

Коротяев, Е. Л., Mantile, A., & Mokeev, D. (2024). Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line. SIAM Journal on Mathematical Analysis, 56(2), 2115-2148. [2]. https://doi.org/10.1137/23m1591104

Vancouver

Коротяев ЕЛ, Mantile A, Mokeev D. Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line. SIAM Journal on Mathematical Analysis. 2024 Mar 5;56(2):2115-2148. 2. https://doi.org/10.1137/23m1591104

Author

Коротяев, Евгений Леонидович ; Mantile, Andrea ; Mokeev, Dmitrii. / Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line. In: SIAM Journal on Mathematical Analysis. 2024 ; Vol. 56, No. 2. pp. 2115-2148.

BibTeX

@article{a7acee9a19d4416b9d6c8278c56be2da,
title = "Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line",
abstract = "Abstract. We consider Schr{\"o}dinger equations with energy-dependent potentials that are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under suitable regularity assumptions. Then, we consider a specific class of energy-dependent Schr{\"o}dinger equations without eigenvalues, defined with Miura potentials and boundary conditions at the origin. We solve the inverse resonance problem in this case and describe sets of isoresonance potentials and boundary condition parameters. Our strategy consists of exploiting a correspondence between Schr{\"o}dinger and Dirac equations on the half-line. As a byproduct, we describe similar sets for Dirac operators and show that the scattering problem for a Schr{\"o}dinger equation or Dirac operator with an arbitrary boundary condition can be reduced to the scattering problem with the Dirichlet boundary condition.",
author = "Коротяев, {Евгений Леонидович} and Andrea Mantile and Dmitrii Mokeev",
year = "2024",
month = mar,
day = "5",
doi = "10.1137/23m1591104",
language = "не определен",
volume = "56",
pages = "2115--2148",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line

AU - Коротяев, Евгений Леонидович

AU - Mantile, Andrea

AU - Mokeev, Dmitrii

PY - 2024/3/5

Y1 - 2024/3/5

N2 - Abstract. We consider Schrödinger equations with energy-dependent potentials that are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under suitable regularity assumptions. Then, we consider a specific class of energy-dependent Schrödinger equations without eigenvalues, defined with Miura potentials and boundary conditions at the origin. We solve the inverse resonance problem in this case and describe sets of isoresonance potentials and boundary condition parameters. Our strategy consists of exploiting a correspondence between Schrödinger and Dirac equations on the half-line. As a byproduct, we describe similar sets for Dirac operators and show that the scattering problem for a Schrödinger equation or Dirac operator with an arbitrary boundary condition can be reduced to the scattering problem with the Dirichlet boundary condition.

AB - Abstract. We consider Schrödinger equations with energy-dependent potentials that are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under suitable regularity assumptions. Then, we consider a specific class of energy-dependent Schrödinger equations without eigenvalues, defined with Miura potentials and boundary conditions at the origin. We solve the inverse resonance problem in this case and describe sets of isoresonance potentials and boundary condition parameters. Our strategy consists of exploiting a correspondence between Schrödinger and Dirac equations on the half-line. As a byproduct, we describe similar sets for Dirac operators and show that the scattering problem for a Schrödinger equation or Dirac operator with an arbitrary boundary condition can be reduced to the scattering problem with the Dirichlet boundary condition.

UR - https://www.mendeley.com/catalogue/64e036e8-b37c-36d2-84a6-1ca33a251b13/

U2 - 10.1137/23m1591104

DO - 10.1137/23m1591104

M3 - статья

VL - 56

SP - 2115

EP - 2148

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 2

M1 - 2

ER -

ID: 126834956