Spectral properties of a class of operators associated with conformal maps in two dimensions |
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Authors: | David Ruelle |
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Institution: | (1) I.H.E.S., 35, Route de Chartres, F-91440 Bures-Sur-Yvette, France |
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Abstract: | Iff is a rational map of the Riemann sphere, define the transfer operator by
Let also be the Banach space of functions for which the second derivatives are measures. Ifg andg satisfies a simple integrability condition (implying thatg vanishes at critical points and multiple poles off) then is a bounded linear operator on . The essential spectral radius of can be estimated and, under suitable conditions, proved to be strictly less than the spectral radius. Similar estimates for more general operators are also obtained. |
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Keywords: | |
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