Selberg Zeta Functions And Transfer Operators: An Experimental Approach To Singular Perturbations (lecture Notes In Mathematics)
by Markus Szymon Fraczek /
2017 / English / EPUB
8.6 MB Download
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.
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.
