Scattering Operator Eisenstein Series Inner Product Formula And Maass Selberg Relations For Kleinian Groups
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Scattering Operator Eisenstein Series Inner Product Formula And Maass Selberg Relations For Kleinian Groups
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Author : Nikolaos Mandouvalos
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Scattering Operator Eisenstein Series Inner Product Formula And Maass Selberg Relations For Kleinian Groups written by Nikolaos Mandouvalos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
In this memoir we have introduced and studied the scattering operator and the Eisenstein series and we have formulated and proved the inner product formula and the "Maass-Selberg" relations for Kleinian groups.
Spectral Theory Of Infinite Area Hyperbolic Surfaces
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Author : David Borthwick
language : en
Publisher: Birkhäuser
Release Date : 2016-07-12
Spectral Theory Of Infinite Area Hyperbolic Surfaces written by David Borthwick and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-12 with Mathematics categories.
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory. This book will serve as a valuable resource for graduate students and researchers from these and other related fields. Review of the first edition: "The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it." (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)
Heat Kernels And Spectral Theory
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Author : E. B. Davies
language : en
Publisher: Cambridge University Press
Release Date : 1989
Heat Kernels And Spectral Theory written by E. B. Davies and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.
Cohomological Theory Of Dynamical Zeta Functions
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Author : Andreas Juhl
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Cohomological Theory Of Dynamical Zeta Functions written by Andreas Juhl and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.
Selberg Trace Formulae And Equidistribution Theorems For Closed Geodesics And Laplace
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Author : Steven Zelditch
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Selberg Trace Formulae And Equidistribution Theorems For Closed Geodesics And Laplace written by Steven Zelditch and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This memoir extends the author's earlier work and gives a generalization of the Selberg trace formula and applications to generalizations of the eigenvalue counting problem and the prime geodesic theorem. As a consequence of these results, he obtains both a proof of the equidistribution theorem for closed geodesics and sharp error estimates. His previous work derived the relevant trace formulae in the compact quotient case, and this paper is concerned largely with the additional complications that occur in the noncompact case, both in terms of deriving the relevant formulae and in estimating various terms.
Kernel Functions Analytic Torsion And Moduli Spaces
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Author : John David Fay
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Kernel Functions Analytic Torsion And Moduli Spaces written by John David Fay and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This memoir is a study of Ray-Singer analytic torsion for hermitian vector bundles on a compact Riemann surface [italic]C. The torsion is expressed through the trace of a modified resolvent. Thus, one can develop perturbation-curvature formulae for the Green-Szegö kernel and also for the torsion in terms of the Ahlfors-Bers complex structure of the Teichmuller space and Mumford complex structure of the moduli space of stable bundles of degree zero on [italic]C.
Vertex Algebras And Integral Bases For The Enveloping Algebras Of Affine Lie Algebras
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Author : Shari A. Prevost
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Vertex Algebras And Integral Bases For The Enveloping Algebras Of Affine Lie Algebras written by Shari A. Prevost and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.
Sum Of Even Powers Of Real Linear Forms
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Author : Bruce Arie Reznick
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Sum Of Even Powers Of Real Linear Forms written by Bruce Arie Reznick and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This work initiates a systematic analysis of the representation of real forms of even degree as sums of powers of linear forms and the resulting implications in real algebraic geometry, number theory, combinatorics, functional analysis, and numerical analysis. The proofs utilize elementary techniques from linear algebra, convexity, number theory, and real algebraic geometry and many explicit examples and relevant historical remarks are presented.
Seminaire De Probabilites Xxxv
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Author : J. Azema
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-04-10
Seminaire De Probabilites Xxxv written by J. Azema and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-10 with Mathematics categories.
Researchers and graduate students in the theory of stochastic processes will find in this 35th volume some thirty articles on martingale theory, martingales and finance, analytical inequalities and semigroups, stochastic differential equations, functionals of Brownian motion and of Lévy processes. Ledoux's article contains a self-contained introduction to the use of semigroups in spectral gaps and logarithmic Sobolev inequalities; the contribution by Emery and Schachermayer includes an exposition for probabilists of Vershik's theory of backward discrete filtrations.
Bulletin New Series Of The American Mathematical Society
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Author :
language : en
Publisher:
Release Date : 1991
Bulletin New Series Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Electronic journals categories.