ar X iv : m at h / 03 02 16 5 v 1 [ m at h . O A ] 1 3 Fe b 20 03 THE WAVELET GALERKIN OPERATOR
نویسنده
چکیده
The wavelet Galerkin operator appears in several different contexts such as wavelets (see for example [Law91b], [Dau95], [CoDa96], [LLS96], [CoRa90]), ergodic theory and g-measures ([Kea82]) or quantum statistical mechanics ([Rue68]). For some of the applications of the Ruelle operator we refer the reader to the book by V. Baladi [Bal00]. It also bears many different names in the literature: the Ruelle operator, the Perron-Frobenius-Ruelle operator, the Ruelle-Araki operator, the Sinai-Bowen-Ruelle operator, the transfer operator and several others. We used the name wavelet Galerkin operator as suggested in [Law91b], because of its close connection to wavelets that we will be using in the sequel. We will also use the name Ruelle operator and transfer operator. The Ruelle operator considered in this paper is defined by
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