Standard

Trace formulas for Schrödinger operators with complex potentials on a half line. / Korotyaev, Evgeny.

In: Letters in Mathematical Physics, Vol. 110, No. 1, 01.2020, p. 1-20.

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

Harvard

Korotyaev, E 2020, 'Trace formulas for Schrödinger operators with complex potentials on a half line', Letters in Mathematical Physics, vol. 110, no. 1, pp. 1-20. https://doi.org/10.1007/s11005-019-01210-x

APA

Korotyaev, E. (2020). Trace formulas for Schrödinger operators with complex potentials on a half line. Letters in Mathematical Physics, 110(1), 1-20. https://doi.org/10.1007/s11005-019-01210-x

Vancouver

Korotyaev E. Trace formulas for Schrödinger operators with complex potentials on a half line. Letters in Mathematical Physics. 2020 Jan;110(1):1-20. https://doi.org/10.1007/s11005-019-01210-x

Author

Korotyaev, Evgeny. / Trace formulas for Schrödinger operators with complex potentials on a half line. In: Letters in Mathematical Physics. 2020 ; Vol. 110, No. 1. pp. 1-20.

BibTeX

@article{8f42d5403bf84bd4ba3c8fafeee81c55,
title = "Trace formulas for Schr{\"o}dinger operators with complex potentials on a half line",
abstract = "We consider Schr{\"o}dinger operators with complex-valued decaying potentials on the half line. Such operator has essential spectrum on the half line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half line. We determine trace formula: sum of imaginary part of these eigenvalues plus some singular measure plus some integral from the Jost function. Moreover, we estimate sum of imaginary part of eigenvalues and singular measure in terms of the norm of potentials. In addition, we get bounds on the total number of eigenvalues, when the potential is compactly supported.",
keywords = "Complex potentials, Trace formulas, EIGENVALUES, TERMS, ASYMPTOTICS",
author = "Evgeny Korotyaev",
note = "Funding Information: Evgeny Korotyaev is grateful to Ari Laptev for discussions about the Schr{\"o}dinger operators with complex potentials. He is also grateful to Alexei Alexandrov (St. Petersburg) for discussions and useful comments about Hardy spaces. Our study was supported by the RSF grant No 18-11-00032. Finally, we would like to thank the referees for thoughtful comments that helped us to improve the manuscript.",
year = "2020",
month = jan,
doi = "10.1007/s11005-019-01210-x",
language = "English",
volume = "110",
pages = "1--20",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Trace formulas for Schrödinger operators with complex potentials on a half line

AU - Korotyaev, Evgeny

N1 - Funding Information: Evgeny Korotyaev is grateful to Ari Laptev for discussions about the Schrödinger operators with complex potentials. He is also grateful to Alexei Alexandrov (St. Petersburg) for discussions and useful comments about Hardy spaces. Our study was supported by the RSF grant No 18-11-00032. Finally, we would like to thank the referees for thoughtful comments that helped us to improve the manuscript.

PY - 2020/1

Y1 - 2020/1

N2 - We consider Schrödinger operators with complex-valued decaying potentials on the half line. Such operator has essential spectrum on the half line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half line. We determine trace formula: sum of imaginary part of these eigenvalues plus some singular measure plus some integral from the Jost function. Moreover, we estimate sum of imaginary part of eigenvalues and singular measure in terms of the norm of potentials. In addition, we get bounds on the total number of eigenvalues, when the potential is compactly supported.

AB - We consider Schrödinger operators with complex-valued decaying potentials on the half line. Such operator has essential spectrum on the half line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half line. We determine trace formula: sum of imaginary part of these eigenvalues plus some singular measure plus some integral from the Jost function. Moreover, we estimate sum of imaginary part of eigenvalues and singular measure in terms of the norm of potentials. In addition, we get bounds on the total number of eigenvalues, when the potential is compactly supported.

KW - Complex potentials

KW - Trace formulas

KW - EIGENVALUES

KW - TERMS

KW - ASYMPTOTICS

UR - http://www.scopus.com/inward/record.url?scp=85073950209&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/9e4a2c83-c726-3cf6-8af0-780c4d9fea61/

U2 - 10.1007/s11005-019-01210-x

DO - 10.1007/s11005-019-01210-x

M3 - Article

AN - SCOPUS:85073950209

VL - 110

SP - 1

EP - 20

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 1

ER -

ID: 48515797