On the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operators

Aleksey Kostenko; Gerald Teschl

doi:10.1016/j.jde.2010.10.026

On the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operators

Aleksey Kostenko
, Gerald Teschl

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

Abstract

We investigate the singular Weyl-Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x)∈L1(0,1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations.

Original language	English
Pages (from-to)	3701-3739
Number of pages	39
Journal	Journal of Differential Equations
Volume	250
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2010.10.026
Publication status	Published - 1 May 2011
Externally published	Yes

Keywords

Bessel operators
Primary
Schrödinger operators
Secondary
Weyl-Titchmarsh theory

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10.1016/j.jde.2010.10.026

https://arrow.tudublin.ie/scschmatart/252Licence: CC BY-NC-SA

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title = "On the singular Weyl-Titchmarsh function of perturbed spherical Schr{\"o}dinger operators",

abstract = "We investigate the singular Weyl-Titchmarsh m-function of perturbed spherical Schr{\"o}dinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x)∈L1(0,1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations.",

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AU - Kostenko, Aleksey

AU - Teschl, Gerald

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N2 - We investigate the singular Weyl-Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x)∈L1(0,1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations.

AB - We investigate the singular Weyl-Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x)∈L1(0,1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations.

KW - Bessel operators

KW - Primary

KW - Schrödinger operators

KW - Secondary

KW - Weyl-Titchmarsh theory

UR - https://www.scopus.com/pages/publications/79952037693

U2 - 10.1016/j.jde.2010.10.026

DO - 10.1016/j.jde.2010.10.026

M3 - Article

SN - 0022-0396

VL - 250

SP - 3701

EP - 3739

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 9

ER -

On the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operators

Abstract

Keywords

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