Free Delivery Over $100
|
|
|||
|
||||
OverviewEigenfunctions 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. Full Product DetailsAuthor: Steve ZelditchPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.525kg ISBN: 9781470410377ISBN 10: 1470410370 Pages: 394 Publication Date: 30 December 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Geometric preliminaries Main results Model spaces of constant curvature Local structure of eigenfunctions Hadamard parametrics on Riemannian manifolds Lagrangian distributions and Fourier integral operators Small time wave group and Weyl asymptotics Matrix elements $L^p$ norms Quantum integrable systems Restriction theorems Nodal sets: Real domain Eigenfunctions in the complex domain Index.ReviewsAuthor InformationSteve Zelditch, Northwestern University, Evanston, IL. Tab Content 6Author Website:Countries AvailableAll regions |
||||
