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Anniversary Volume on Approximation Theory and Functional Analysis pp 119–134Cite as

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Invariant Function Spaces Connected with the Holomorphic Discrete Series

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Abstract

The theory of Möbius invariant spaces of holomorphic functions, as developed by Arazy, Fisher, and others, is briefly reviewed. Then an extension of it (connected with the discrete holomorphic series) is outlined. The main object of the lecture is however the advancement of the thesis that the systematic use of group invariant spaces is a useful point of view in Analysis, and we illustrate it on the hand of several concrete applications. In particular, we give a new simple proof of the trace ideal criterion for Hankel operators (Peller’s theorem) in the case 1 < p < ∞.

Joint work with Jonathan Arazy, Stephen Fisher, Svante Janson; I am solely responsible for any possible mistakes in this messy compilation, prepared on the occasion of the conference Functional Analysis and Approximation (Oberwohlfach, July 30 - Aug. 6, 1983). A somewhat more detailed version is available in the Lund report series.

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References

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Authors and Affiliations

  1. Matematiska Institutionen, Lunds Universitet, S-220 07, Lund, Sweden

    Jaak Peetre

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  1. Jaak Peetre
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Editors and Affiliations

  1. Lehrstuhl A für Mathematik, Rhein.-Westf. Techn. Hochschule Aachen, Templergraben 55, D-5100, Aachen, Germany

    P. L. Butzer  & R. L. Stens  & 

  2. József Attila University, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

    B. Sz.-Nagy

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© 1984 Springer Basel AG

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Peetre, J. (1984). Invariant Function Spaces Connected with the Holomorphic Discrete Series. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_12

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  • DOI: https://doi.org/10.1007/978-3-0348-5432-0_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5434-4

  • Online ISBN: 978-3-0348-5432-0

  • eBook Packages: Springer Book Archive

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