The Heat Kernel and Theta Inversion on SL2(C)

• Main Authors: Jorgenson, Jay (Author), Lang, Serge (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2008.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebra.; Group theory.; Mathematical analysis.; Analysis (Mathematics).; Number theory.; Number Theory.; Group Theory and Generalizations.; Analysis.

The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL2(C). The authors begin with the realization of the heat kernel on SL2(C) through spherical transform, from which one ma...

Table of Contents:

• Gaussians, Spherical Inversion, and the Heat Kernel
• Spherical Inversion on SL2(C)
• The Heat Gaussian and Heat Kernel
• QED, LEG, Transpose, and Casimir
• Enter ?: The General Trace Formula
• Convergence and Divergence of the Selberg Trace
• The Cuspidal and Noncuspidal Traces
• The Heat Kernel on ?\G/K
• The Fundamental Domain
• ?-Periodization of the Heat Kernel
• Heat Kernel Convolution on (?\G/K)
• Fourier-Eisenstein Eigenfunction Expansions
• The Tube Domain for ??
• The ?/U-Fourier Expansion of Eisenstein Series
• Adjointness Formula and the ?\G-Eigenfunction Expansion
• The Eisenstein-Cuspidal Affair
• The Eisenstein Y-Asymptotics
• The Cuspidal Trace Y-Asymptotics
• Analytic Evaluations.