Discrete spectrum and principal functions of non-selfadjoint differential operator

Tunca, Gülen Başcanbaz, and Bairamov, Elgiz. "Discrete spectrum and principal functions of non-selfadjoint differential operator." Czechoslovak Mathematical Journal 49.4 (1999): 689-700. <http://eudml.org/doc/30516>.

@article{Tunca1999,
abstract = {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.},
author = {Tunca, Gülen Başcanbaz, Bairamov, Elgiz},
journal = {Czechoslovak Mathematical Journal},
keywords = {discrete spectrum; eigenvalue; spectral singularity; one-dimensional Schrödinger operator},
language = {eng},
number = {4},
pages = {689-700},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Discrete spectrum and principal functions of non-selfadjoint differential operator},
url = {http://eudml.org/doc/30516},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Tunca, Gülen Başcanbaz
AU - Bairamov, Elgiz
TI - Discrete spectrum and principal functions of non-selfadjoint differential operator
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 4
SP - 689
EP - 700
AB - 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.
LA - eng
KW - discrete spectrum; eigenvalue; spectral singularity; one-dimensional Schrödinger operator
UR - http://eudml.org/doc/30516
ER -