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Wiener's tauberian theorem for spherical functions on the automorphism group of the unit disk

Yaakov Ben Natan Department of Mathematics Technion, Israel Institute of Technology Yoav Benyamini Department of Mathematics Technion, Israel Institute of Technology H»kan Hendenmalm Department of Mathematics, Uppsala University Yitzhak Weit Department of Mathematics, University of Haifa

TBD mathscidoc:1701.332855

Arkiv for Matematik, 34, (2), 199-224, 1995.8
Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the convolution algebra of spherical integrable functions on the (conformal) automorphism group of the unit disk to be dense, or to have as closure the closed ideal of functions with integral 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 Agranovskii).
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@inproceedings{yaakov1995wiener's,
  title={Wiener's tauberian theorem for spherical functions on the automorphism group of the unit disk},
  author={Yaakov Ben Natan, Yoav Benyamini, H»kan Hendenmalm, and Yitzhak Weit},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203548419855664},
  booktitle={Arkiv for Matematik},
  volume={34},
  number={2},
  pages={199-224},
  year={1995},
}
Yaakov Ben Natan, Yoav Benyamini, H»kan Hendenmalm, and Yitzhak Weit. Wiener's tauberian theorem for spherical functions on the automorphism group of the unit disk. 1995. Vol. 34. In Arkiv for Matematik. pp.199-224. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203548419855664.
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