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On a Projection from One Co – Invariant Subspace onto Another in Character – Automorphic Hardy Space on a Multiply Connected Domain
Author(s) -
Fedorov Sergei
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200009)217:1<53::aid-mana53>3.0.co;2-z
Subject(s) - mathematics , linear subspace , invertible matrix , pure mathematics , invariant (physics) , invariant subspace , subspace topology , projection (relational algebra) , hardy space , mathematical analysis , automorphic form , character (mathematics) , orthogonal basis , geometry , algorithm , physics , quantum mechanics , mathematical physics
In a case of a theory in a unit disk the solution of a problem on the invertibility of an orthogonal projection from one co–invariant subspace of the shift operator onto another turned out to be essential for the solution of the problem on the Riesz basis property of the reproducing kernels and in particular for the solution of the problem on the basis of exponentials in L 2 space on a segment. In the present paper we are dealing with the similar problems in harmonic analysis on a finitely connected domain. Namely we obtain necessary and sufficient conditions for the invertibility of an orthogonal projection from one co – invariant subspace of character – automorphic Hardy space in the domain onto another. The given condition has a form of a Muckenhoupt condition for a certain weight on the boundary of the domain, but essentially depends on a character. Namely, for two fixed character – automorphic inner functions, which define the co – invariant subspaces, the projection may be invertible for one character and not invertible for another.