Fourier Integrals in Classical Analysis (Cambridge Tracts in Mathematics) - Christopher D. Sogge, Christopher Donald Sogge (1993)
ISBN 0521434645
Subject Fourier integral operators; Fourier series
Publisher Cambridge University Press
Publication Date 2/26/1993
Format Hardcover (237 x 161 mm)
Language e
Fourier Integrals in Classical Analysis is an advanced treatment 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, 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.
Personal Details
Collection Status In Collection
Index 146
Read It Yes
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Product Details
LoC Classification QA404 .S64 1993
Dewey 515/.2433
Cover Price $95.00
No. of Pages 248
Errata slip inserted.