The Spectrum of the Laplacian
This chapter gives a self-contained introduction into the Laplacian of compact Riemann surfaces. We prove the spectral theorem using the heat kernel which is given explicitly in Section 7.4 for the hyperbolic plane and in Section 7.5 for the compact quotients. As a tool we use the Abel transform which is introduced in Section 7.3. This transform will again show up in Chapter 9 in connection with Selberg’s trace formula.
KeywordsFundamental Solution Heat Equation Heat Kernel Hyperbolic Plane Compact Riemann Surface
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