The Characteristic Function for Complex Doubly Infinite Jacobi Matrices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F17%3A00312833" target="_blank" >RIV/68407700:21240/17:00312833 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs00020-017-2357-y" target="_blank" >https://link.springer.com/article/10.1007%2Fs00020-017-2357-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00020-017-2357-y" target="_blank" >10.1007/s00020-017-2357-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Characteristic Function for Complex Doubly Infinite Jacobi Matrices

Popis výsledku v původním jazyce

We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a characteristic function, is associated with it. It is shown that the point spectrum of the corresponding Jacobi operator restricted to a suitable domain coincides with the zero set of the characteristic function. Also, coincidence regarding the order of a zero of the characteristic function and the algebraic multiplicity of the corresponding eigenvalue is proved. Further, formulas for the entries of eigenvectors, generalized eigenvectors, a summation identity for eigenvectors, and matrix elements of the resolvent operator are provided. The presented method is illustrated by several concrete examples.

Název v anglickém jazyce

The Characteristic Function for Complex Doubly Infinite Jacobi Matrices

Popis výsledku anglicky

We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a characteristic function, is associated with it. It is shown that the point spectrum of the corresponding Jacobi operator restricted to a suitable domain coincides with the zero set of the characteristic function. Also, coincidence regarding the order of a zero of the characteristic function and the algebraic multiplicity of the corresponding eigenvalue is proved. Further, formulas for the entries of eigenvectors, generalized eigenvectors, a summation identity for eigenvectors, and matrix elements of the resolvent operator are provided. The presented method is illustrated by several concrete examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Integral Equations and Operator Theory

ISSN

0378-620X

e-ISSN

1420-8989

Svazek periodika

88

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

34

Strana od-do

501-534

Kód UT WoS článku

000409890100004

EID výsledku v databázi Scopus

2-s2.0-85016112938