TY  - BOOK
AU  - Sogge,Christopher D.
TI  - Fourier integrals in classical analysis
T2  - Cambridge tracts in mathematics
SN  - 9781316341186 (ebook)
AV  - QA404 .S64 2017
U1  - 515/.723 23
PY  - 2017///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Fourier series
KW  - Fourier integral operators
KW  - Fourier analysis
N1  - Title from publisher's bibliographic system (viewed on 25 May 2017)
N2  - 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
UR  - https://doi.org/10.1017/9781316341186
ER  -