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m-Berezin Transform on the Polydisk

✍ Scribed by Kyesook Nam; Dechao Zheng

Book ID
105760311
Publisher
SP Birkhäuser Verlag Basel
Year
2005
Tongue
English
Weight
269 KB
Volume
56
Category
Article
ISSN
0378-620X

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📜 SIMILAR VOLUMES

Functions Invariant under the Berezin Tr
Functions Invariant under the Berezin Transform
✍ M. Englis 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 587 KB

We show that a bounded function \(f\) satisfies \(B f=f\), 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 Z. Cučković, Integral Equations Operator Theory 14 (1991), 1-12; W

Invariant Operators and the Berezin Tran
Invariant Operators and the Berezin Transform on Cartan Domains
✍ Miroslav Engliš 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 651 KB

Let R be an irreducible Cartan domain of rank r and genus p and B, (Y > p -1) be the Berezin transform on R. It is known that as v tends to infinity, the Berezin transform admits the asymptotic expansion B, M C' p,, Q k U k where the Qk'S are certain invariant differential operatorsfor instance, Qo