Eigenfunctions of the Laplacian on a Riemannian Manifold

Eigenfunctions of the Laplacian on a Riemannian Manifold
Author :
Publisher : American Mathematical Soc.
Total Pages : 410
Release :
ISBN-10 : 9781470410377
ISBN-13 : 1470410370
Rating : 4/5 (77 Downloads)

Book Synopsis Eigenfunctions of the Laplacian on a Riemannian Manifold by : Steve Zelditch

Download or read book Eigenfunctions of the Laplacian on a Riemannian Manifold written by Steve Zelditch and published by American Mathematical Soc.. This book was released on 2017-12-12 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.


Eigenfunctions of the Laplacian on a Riemannian Manifold Related Books

Eigenfunctions of the Laplacian on a Riemannian Manifold
Language: en
Pages: 410
Authors: Steve Zelditch
Categories: Mathematics
Type: BOOK - Published: 2017-12-12 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an
The Laplacian on a Riemannian Manifold
Language: en
Pages: 190
Authors: Steven Rosenberg
Categories: Mathematics
Type: BOOK - Published: 1997-01-09 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Hangzhou Lectures on Eigenfunctions of the Laplacian
Language: en
Pages: 205
Authors: Christopher D. Sogge
Categories: Mathematics
Type: BOOK - Published: 2014-03-10 - Publisher: Princeton University Press

DOWNLOAD EBOOK

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Ch
Eigenvalues in Riemannian Geometry
Language: en
Pages: 379
Authors: Isaac Chavel
Categories: Mathematics
Type: BOOK - Published: 1984-11-07 - Publisher: Academic Press

DOWNLOAD EBOOK

The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and
Spectral Geometry Of The Laplacian: Spectral Analysis And Differential Geometry Of The Laplacian
Language: en
Pages: 310
Authors: Hajime Urakawa
Categories: Mathematics
Type: BOOK - Published: 2017-06-02 - Publisher: World Scientific

DOWNLOAD EBOOK

The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian m