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＜電子ブック＞
Selberg Zeta Functions and Transfer Operators : An Experimental Approach to Singular Perturbations / by Markus Szymon Fraczek
(Lecture Notes in Mathematics. ISSN:16179692 ; 2139)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
大きさ	XV, 354 p. 71 illus., 43 illus. in color : online resource
著者標目	*Fraczek, Markus Szymon author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Mathematics—Data processing LCSH:Approximation theory LCSH:Functions of complex variables LCSH:Special functions LCSH:Dynamical systems FREE:Number Theory FREE:Computational Mathematics and Numerical Analysis FREE:Approximations and Expansions FREE:Functions of a Complex Variable FREE:Special Functions FREE:Dynamical Systems
一般注記	This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spaces HTTP:URL=https://doi.org/10.1007/978-3-319-51296-9

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