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Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Wiener's Tauberian theorem in $ L_1(G//K)$ and harmonic functions in the unit disk

Author(s): Y. Ben Natan; Y. Benyamini; H. Hedenmalm; Y. Weit
Journal: Bull. Amer. Math. Soc. 32 (1995), 43-49.
MathSciNet review: 1273399
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Abstract | References | Additional information

Abstract: Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal I in $ {L^1}(G//K)$, the space of radial integrable functions on $ G = SU(1,1)$, so that $ I = {L^1}(G//K)$ or $ I = L_0^1(G//K)$--the ideal of $ {L^1}(G//K)$ functions whose integral is zero. This is then used to prove a generalization of Furstenberg's theorem which characterizes harmonic functions on the unit disk by a mean value property and a "two circles" Morera type theorem (earlier announced by Agranovskiĭ).

References:

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Additional Information:

DOI: 10.1090/S0273-0979-1995-00554-9
PII: S 0273-0979(1995)00554-9
Keywords: Spherical functions, $ SU(1,1)$, Resolvent transform, Spectral synthesis, Wiener's theorem, $ \mu $-harmonic functions, two circles theorems
Copyright of article: Copyright 1995, American Mathematical Society




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