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A Paley–Wiener theorem for Bergman spaces with application to invariant subspaces
Author(s) -
Duren Peter,
GallardoGutiérrez Eva A.,
MontesRodríguez Alfonso
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm026
Subject(s) - mathematics , bergman space , bergman kernel , linear subspace , invariant (physics) , unit disk , pure mathematics , invariant subspace , convolution (computer science) , mathematical analysis , discrete mathematics , mathematical physics , bounded function , machine learning , artificial neural network , computer science
An analogue of the Paley–Wiener theorem is developed for weighted Bergman spaces of analytic functions in the upper half‐plane. The result is applied to show that the invariant subspaces of the shift operator on the standard Bergman space of the unit disk can be identified with those of a convolution Volterra operator on the space L 2 (ℝ + , (1/ t ) dt ).