Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F17%3A00480641" target="_blank" >RIV/61389005:_____/17:00480641 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.7153/oam-2017-11-64" target="_blank" >http://dx.doi.org/10.7153/oam-2017-11-64</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.7153/oam-2017-11-64" target="_blank" >10.7153/oam-2017-11-64</a>

Result language

angličtina

Original language name

Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions

Original language description

We perform the spectral analysis of a family of Jacobi operators J(alpha) depending on a complex parameter alpha. If |alpha| not equal 1 the spectrum of J(alpha) is discrete and formulas for eigenvalues and eigenvectors are established in terms of elliptic integrals and Jacobian elliptic functions. If |alpha| = 1, alpha not equal perpendicular to 1, the essential spectrum of J(alpha) covers the entire complex plane. In addition, a formula for theWeyl m-function as well as the asymptotic expansions of solutions of the difference equation corresponding to J(alpha) are obtained. Finally, the completeness of eigenvectors and Rodriguez-like formulas for orthogonal polynomials, studied previously by Carlitz, are proved.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2017

Confidentiality

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

Name of the periodical

Operators and Matrices

ISSN

1846-3886

e-ISSN

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Volume of the periodical

11

Issue of the periodical within the volume

4

Country of publishing house

HR - CROATIA

Number of pages

28

Pages from-to

901-928

UT code for WoS article

000413118300001

EID of the result in the Scopus database

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