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- W2027650067 abstract "We show that a bounded function f satisfies Bf = f, where B is the Berezin tranform on the unit disc (defined in (2) below), if and only if f is harmonic. There is an equivalent formulation of this result [S. Axler and Ž. Čučković, Integral Equations Operator Theory14 (1991), 1-12; W. Rudin, Function Theory in the Unit Ball of CN, Springer-Verlag, New York/Berlin, 1980]: If f is bounded and satifies the invariant version of the area mean value property, then f is harmonic. The main tool employed is Fourier analysis on the Lie group of all Möbius transformations." @default.
- W2027650067 created "2016-06-24" @default.
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- W2027650067 date "1994-04-01" @default.
- W2027650067 modified "2023-09-30" @default.
- W2027650067 title "Functions Invariant under the Berezin Transform" @default.
- W2027650067 doi "https://doi.org/10.1006/jfan.1994.1048" @default.
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