Generalized Krein Formula, Determinants, and Selberg Zeta Function in Even Dimension

For a class of even dimensional asymptotically hyperbolic (AH) manifolds, we develop a generalized Birman-Krein theory to study scattering asymptotics and, when the curvature is constant, to analyze the Selberg zeta function. The main objects we construct for an AH manifold (X, g) are, on the one ha...

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Bibliographic Details
Published in:	American journal of mathematics Vol. 131; no. 5; pp. 1359 - 1417
Main Author:	Guillarmou, Colin
Format:	Journal Article
Language:	English
Published:	Baltimore, MD Johns Hopkins University Press 01.10.2009
Subjects:	Algebra Continuous spectra Coordinate systems Differential operators Dimensional analysis Dynamical systems Exact sciences and technology Fourier transformations General mathematics General, history and biography Infinity Laplacians Mathematical analysis Mathematical functions Mathematical manifolds Mathematical problems Mathematics Number theory Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Riemann manifold Sciences and techniques of general use Several complex variables and analytic spaces Theory Topological manifolds Spectral function Zero Determinant Functional equation Eigenvalue Scattering operator Mathematics Laplacian Kernel method Scattering theory Functional Kernels Trace Manifold Multiplicity Counting function Zeta function Generalized manifold Resonance Asymptotic approximation Curvature Quotient Pole
ISSN:	0002-9327, 1080-6377, 1080-6377
Online Access:	Get full text
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