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Q&A | February 27, 2014

Rene Denfeld: IMG Powell’s Q&A: Rene Denfeld



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    Rene Denfeld 9780062285508

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Cambridge Tracts in Mathematics #105: Fourier Integrals in Classical Analysis

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Cambridge Tracts in Mathematics #105: Fourier Integrals in Classical Analysis Cover

 

Synopses & Reviews

Publisher Comments:

Fourier 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 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. This book will be of vital interest to advanced graduate students and research mathematicians working in analysis.

Synopsis:

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.

Description:

Includes bibliographical references (p. [230]-236) and index.

Table of Contents

Background; 1. Stationary phase; 2. Non-homogeneous oscillatory integral operators; 3. Pseudo-differential operators; 4. The half-wave operator and functions of pseudo-differential operators; 5. Lp estimates of eigenfunctions; 6. Fourier integral operators; 7. Local smoothing of Fourier integral operators; Appendix. Lagrangian subspaces of T*IRn.

Product Details

ISBN:
9780521434645
Editor:
Bollobas, B.
Author:
Sogge, Christopher D.
Editor:
Bollobas, B.
Editor:
Bollobas, Bela
Author:
Kirwan, F.
Author:
Katok, A.
Author:
Soggie, Christopher D.
Author:
Bollobas, B.
Author:
Fulton, W.
Author:
Sarnak, P.
Publisher:
Cambridge University Press
Location:
Cambridge England ;
Subject:
Differential Equations
Subject:
Probability
Subject:
Infinity
Subject:
Fourier series
Subject:
Fourier integral operators.
Subject:
Probability & Statistics - General
Subject:
Fourier series Fourier series
Subject:
Mathematics - General
Edition Description:
Hardcover
Series:
Cambridge Tracts in Mathematics (Hardcover)
Series Volume:
9339105
Publication Date:
19930231
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
252
Dimensions:
9.35x6.34x.85 in. 1.17 lbs.

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Health and Self-Help » Health and Medicine » History of Medicine
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Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Cambridge Tracts in Mathematics #105: Fourier Integrals in Classical Analysis New Hardcover
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Product details 252 pages Cambridge University Press - English 9780521434645 Reviews:
"Synopsis" by , 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.
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