Discrete spectrum and principal functions of non-selfadjoint differential operator

Title:

Discrete spectrum and principal functions of non-selfadjoint differential operator

Creator:

Tunca, Gülen Başcanbaz and Bairamov, Elgiz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:19bc4cb3-1f09-43fa-81a6-44363442643c
uuid:19bc4cb3-1f09-43fa-81a6-44363442643c

Subject:

math, non-selfadjoint differential operator, and spectral singularities

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this article, we consider the operator $L$ defined by the differential expression \[ \ell (y)=-y^{\prime \prime }+q(x) y ,\quad - \infty < x < \infty \] in $L_2(-\infty ,\infty)$, where $q$ is a complex valued function. Discussing the spectrum, we prove that $L$ has a finite number of eigenvalues and spectral singularities, if the condition \[ \sup _{-\infty < x < \infty} \Big \lbrace \exp \bigl (\epsilon \sqrt{|x|}\bigr ) |q(x)|\Big \rbrace < \infty, \quad \epsilon > 0 \] holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

689-700

Source:

Czechoslovak Mathematical Journal | 1999 Volume:49 | Number:4

Harvested from:

CDK

Metadata only:

false