The Heat Kernel and Theta Inversion on SL2(C)

Authors:

ISBN: 978-0-387-38031-5 (Print) 978-0-387-38032-2 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-x

  2. Gaussians, Spherical Inversion, and the Heat Kernel

    1. No Access

      Book Chapter

      Pages 1-9

      Introduction

    2. No Access

      Book Chapter

      Pages 13-43

      Spherical Inversion on SL2(C)

    3. No Access

      Book Chapter

      Pages 45-66

      The Heat Gaussian and Heat Kernel

    4. No Access

      Book Chapter

      Pages 67-81

      QED, LEG, Transpose, and Casimir

  3. Enter Γ: The General Trace Formula

    1. No Access

      Book Chapter

      Pages 85-95

      Convergence and Divergence of the Selberg Trace

    2. No Access

      Book Chapter

      Pages 97-114

      The Cuspidal and Noncuspidal Traces

  4. The Heat Kernel on Γ\G/K

    1. No Access

      Book Chapter

      Pages 117-134

      The Fundamental Domain

    2. No Access

      Book Chapter

      Pages 135-150

      Γ-Periodization of the Heat Kernel

    3. No Access

      Book Chapter

      Pages 151-163

      Heat Kernel Convolution on \(L_{{\rm{cusp}}}^2 \) (Γ\G/K)

  5. Fourier-Eisenstein Eigenfunction Expansions

    1. No Access

      Book Chapter

      Pages 167-189

      The Tube Domain for Γ∞

    2. No Access

      Book Chapter

      Pages 191-222

      The Γ/U-Fourier Expansion of Eisenstein Series

    3. No Access

      Book Chapter

      Pages 223-240

      Adjointness Formula and the Γ\G-Eigenfunction Expansion

  6. The Eisenstein-Cuspidal Affair

    1. No Access

      Book Chapter

      Pages 243-259

      The Eisenstein Y-Asymptotics

    2. No Access

      Book Chapter

      Pages 261-286

      The Cuspidal Trace Y-Asymptotics

    3. No Access

      Book Chapter

      Pages 287-309

      Analytic Evaluations

  7. Back Matter

    Pages 311-319