Modular multiplicative inverse: Difference between revisions

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In the [[mathematics|mathematical]] field of [[complex analysis]], the '''Bloch space''', named after [[André Bloch (mathematician)|André Bloch]] and denoted <math>\mathcal{B}</math> or ℬ, is the space of [[holomorphic function]]s ''f'' defined on the [[open set|open]] [[unit disc]] '''D''' in the complex plane, such that the function
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: <math>(1-|z|^2)|f^\prime(z)|</math>
 
is bounded.<ref>{{eom|last=Wiegerinck|first=J.|id=Bloch_function|title=Bloch function}}</ref> <math>\mathcal{B}</math> is a [[Banach space]], with the norm defined by
 
: <math> \|f\|_\mathcal{B} = |f(0)| + \sup_{z \in \mathbf{D}} (1-|z|^2) |f'(z)|. </math>
 
This is referred to as the '''Bloch norm''' and the elements of the Bloch space are called '''Bloch functions'''.
 
==Notes==
{{Reflist}}
 
{{DEFAULTSORT:Bloch Space}}
[[Category:Complex analysis]]
 
 
{{Mathanalysis-stub}}

Revision as of 03:10, 2 March 2014

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