en>RonnieBrown: /* References */ additional references

2012-06-21T16:24:11Z

References: additional references

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In [[mathematics]] — specifically, in [[complex analysis]] — the '''Berezin transform''' is an [[integral operator]] acting on functions defined on the [[open set|open]] [[unit disk]] ''D'' of the [[complex plane]] '''C'''. Formally, for a function ''f'' : ''D'' → '''C''', the '''Berezin transform''' of ''f'' is a new function ''Bf'' : ''D'' → '''C''' defined at a point ''z'' ∈ ''D'' by

:<math>(B f)(z) = \int_{D} \frac{(1 - | z |^{2})^{2}}{| 1 - z \bar{w} |^{4}} f(w) \, \mathrm{dA} (w),</math>

where {{overline|''w''}} denotes the [[complex conjugate]] of ''w'' and <math>dA</math> is the area measure. It is named after [[Felix Alexandrovich Berezin]].

==References==

* {{cite book
| last = Hedenmalm
| first = Haakan
| coauthors = Korenblum, Boris and Zhu, Kehe
| title = Theory of Bergman spaces
| series= Graduate Texts in Mathematics | volume=199
| publisher = Springer-Verlag
| location = New York
| year = 2000
| pages = 28–51
| isbn = 0-387-98791-6
| mr = 1758653
}}

==External links==
* {{MathWorld|urlname=BerezinTransform|title=Berezin transform}}

[[Category:Complex analysis]]
[[Category:Operator theory]]

{{mathanalysis-stub}}

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en>RonnieBrown: /* References */ additional references