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 language | English |
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Title of host publication | Operator Theory |
Subtitle of host publication | Advances and Applications |
Publisher | Springer Science and Business Media Deutschland GmbH |
Pages | 535-581 |
Number of pages | 47 |
DOIs | |
State | Published - 2020 |
Externally published | Yes |
Publication series
Name | Operator Theory: Advances and Applications |
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Volume | 280 |
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.
Funders | Funder number |
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Austrian Science Fund | P29363-N32 |
Keywords
- Akhiezer-Levin condition
- Automorphic hardy space
- Fuchsian group
- Green function
- Martin function
- Regular denjoy domain
- Widom domain