Heat kernel and analysis on manifolds : AMSIP volume 47

By: Grigoryan, AMaterial type: Computer fileComputer fileSeries: AMS/IP Studies in Advanced Mathematics ; v. 47Publication details: Providence, R.I. :;[Somerville, Mass.] : American Mathematical Society : International Press, c2009Description: 1 online resource (xvii, 482 p. : ill.)ISBN: 9781470417505 (online)Subject(s): Gaussian processes | Heat equation | Kernel functions | Riemannian manifoldsLOC classification: QA377Online resources: Click here to access online
Contents:
Laplace operator and the heat equation in
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Laplace operator and the heat equation in mathbb {R}^n ; Function spaces in mathbb {R}^n ; Laplace operator on a Riemannian manifold ; Laplace operator and heat equation in ^{2}(M) ; Weak maximum principle and related topics ; Regularity theory in mathbb {R}^n ; The heat kernel on a manifold ; Positive solutions ; Heat kernel as a fundamental solution ; Spectral properties ; Distance function and completeness ; Gaussian estimates in the integrated form ; Green function and Green operator ; Ultracontractive estimates and eigenvalues ; Pointwise Gaussian estimates I ; Pointwise Gaussian estimates II ; Appendix A. Reference material

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