Martin functions of fuchsian groups and character automorphic subspaces of the hardy space in the upper half plane

A. Kheifets, P. Yuditskii

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations

Abstract

We establish exact conditions for non triviality of all subspaces of the standard Hardy space in the upper half plane, that consist of the character automorphic functions with respect to the action of a discrete subgroup of SL2(ℝ). Such spaces are the natural objects in the context of the spectral theory of almost periodic differential operators and in the asymptotics of the approximations by entire functions. A naive idea: it should be completely parallel to the celebrated Widom characterization for Hardy spaces on Riemann surfaces with a minor modification, namely, one has to substitute the Green function of the domain with the Martin function.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Pages535-581
Number of pages47
StatePublished - 2020
Externally publishedYes

Publication series

NameOperator Theory: Advances and Applications
Volume280
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Funding

P. Yuditskii was supported by the Austrian Science Fund FWF, project no: P29363-N32.

FundersFunder number
Austrian Science FundP29363-N32

    Keywords

    • Akhiezer-Levin condition
    • Automorphic hardy space
    • Fuchsian group
    • Green function
    • Martin function
    • Regular denjoy domain
    • Widom domain

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