Fourier Integrals in Classical Analysis
By (author) Christopher D. Sogge
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Fourier Integrals in Classical Analysis by Christopher D. Sogge
Book DescriptionFourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author, in particular, studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, at the end, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions.
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Book DetailsISBN: 9780521060974
(228mm x 152mm x 15mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 24-Apr-2008
Country of Publication: United Kingdom
Books By Author Christopher D. Sogge
Hangzhou Lectures on Eigenfunctions of the Laplacian, Paperback (March 2014)
Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. It shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic.
Fourier Integrals in Classical Analysis, Hardback (February 1993)» View all books by Christopher D. Sogge
An advanced monograph concerned with modern treatments of central problems in harmonic analysis.
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