Fourier integrals in classical analysis / Christopher D. Sogge, The Johns Hopkins University.

Format:

Book

Author/Creator:

Sogge, Christopher D. (Christopher Donald), 1960-

Series:

Cambridge tracts in mathematics ; 210.

Cambridge tracts in mathematics ; 210

Language:

English

Subjects (All):

Fourier series.

Fourier integral operators.

Fourier analysis.

Physical Description:

1 online resource (xiv, 334 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2017.

Summary:

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.

Notes:

Title from publisher's bibliographic system (viewed on 25 May 2017).

Includes bibliographical references and index.

ISBN:

1-108-23425-9

1-108-23445-3

1-108-23449-6

1-316-34118-6

1-108-23453-4

1-108-23473-9

1-108-23457-7