Harish-Chandras general Plancherel inversion theorem admits a much shorter presentation for spherical functions. Previous expositions have dealt with a general, wide class of Lie groups. This has made access to the subject difficult for outsiders, who may wish to connect some aspects with several if not all other parts of mathematics. In this book, the essential features of Harish-Chandra theory are exhibited on SLn(R), but hundreds of pages of background are replaced by short direct verifications. The material is accessible to graduate students with no background in Lie groups and...
Harish-Chandras general Plancherel inversion theorem admits a much shorter presentation for spherical functions. Previous expositions have dealt with ...
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2, Z i])SL(2, C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2, C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2, Z i])SL(2, C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the...
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2, Z i...
Examines how analytic number theory and part of the spectral theory of operators are being merged into a more general theory of regularized products of certain sequences satisfying a few basic axioms. This monograph explains how the new theory can be applied to ergodic theory and dynamical systems.
Examines how analytic number theory and part of the spectral theory of operators are being merged into a more general theory of regularized products o...
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of...
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These e...
For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgroups. To a large extent, this book carries out the general results of Harish-Chandra.
For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgro...
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2, Z i])SL(2, C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2, C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2, Z i])SL(2, C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the...
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2, Z i...
