Fourier Integrals in Classical Analysis (Hardcover)

Christopher D. Sogge

ISBN 10: 1107120071 / ISBN 13: 9781107120075

Published by Cambridge University Press, Cambridge, 2017

About this Item

Hardcover. This advanced monograph is 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. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hoermander's propagation of singularities theorem and uses this to prove the Duistermaat-Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff. This advanced monograph, concerned with modern treatments of central problems in harmonic analysis, explores the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. New chapters discuss the Duistermaat-Guillemin theorem and results related to the Kakeya conjecture. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781107120075

Bibliographic Details

• Title: Fourier Integrals in Classical Analysis (Hardcover)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2017
• Language: English
• ISBN 10: 1107120071
• ISBN 13: 9781107120075
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: new

About this title

Synopsis

This advanced monograph is 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. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat–Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.

About the Author

Christopher D. Sogge is the J. J. Sylvester Professor of Mathematics at The John Hopkins University and the editor-in-chief of the American Journal of Mathematics. His research concerns Fourier analysis and partial differential equations. In 2012, he became one of the Inaugural Fellows of the American Mathematical Society. He is also a fellow of the National Science Foundation, the Alfred P. Sloan Foundation and the Guggenheim Foundation, and he is a recipient of the Presidential Young Investigator Award. In 2007, he received the Diversity Recognition Award from The Johns Hopkins University.