Time scale symplectic systems with analytic dependence on spectral parameter

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F15%3A00080616" target="_blank" >RIV/00216224:14310/15:00080616 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1080/10236198.2014.997227" target="_blank" >http://dx.doi.org/10.1080/10236198.2014.997227</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/10236198.2014.997227" target="_blank" >10.1080/10236198.2014.997227</a>

Result language

angličtina

Original language name

Time scale symplectic systems with analytic dependence on spectral parameter

Original language description

This paper is devoted to the study of time scale symplectic systems with polynomial and analytic dependence on the complex spectral parameter lambda. We derive fundamental properties of these systems (including the Lagrange identity) and discuss their connection with systems known in the literature, in particular with linear Hamiltonian systems. In analogy with the linear dependence on lambda, we present a construction of the Weyl disks and determine the number of linearly independent square integrablesolutions. These results extend the discrete time theory considered recently by the authors. To our knowledge, in the continuous time case this concept is new. We also establish the invariance of the limit circle case for a special quadratic dependence on lambda and its extension to two (generally nonsymplectic) time scale systems, which yields new results also in the discrete case. The theory is illustrated by several examples.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2015

Confidentiality

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

Name of the periodical

Journal of Difference Equations and Applications

ISSN

1023-6198

e-ISSN

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Volume of the periodical

21

Issue of the periodical within the volume

3

Country of publishing house

GB - UNITED KINGDOM

Number of pages

31

Pages from-to

209-239

UT code for WoS article

000350570500003

EID of the result in the Scopus database

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