A fixed-point theorem for holomorphic maps
Citation:
R.M. Timoney, S. Dineen, J. F. Feinstein and A. G. O'Farrell 'A fixed-point theorem for holomorphic maps' in Proceedings of the Royal Irish Academy, 94A, 1994, pp 77-84Download Item:
Abstract:
We consider the action on the maximal ideal space M of the algebra H of bounded analytic
functions, induced by an analytic self?map of a complex manifold, X. After some general
preliminaries, we focus on the question of the existence of fixed points for this action,
in the case when X is the open unit disk, D. We classify the fixed?point?free M?obius
transformations, and we show that for an arbitrary analytic map from D into itself, the
induced map has a fixed point, or it restricts to a fixed?point?free M?obius map on some
analytic disk contained in M.
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http://people.tcd.ie/rtimoneyDescription:
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Author: TIMONEY, RICHARD
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Royal Irish AcademyType of material:
Journal ArticleSeries/Report no:
Proceedings of the Royal Irish Academy94A
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Pure & Applied MathematicsMetadata
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