The Resource Fourier integrals in classical analysis, Christopher D. Sogge

Fourier integrals in classical analysis, Christopher D. Sogge

Label
Fourier integrals in classical analysis
Title
Fourier integrals in classical analysis
Statement of responsibility
Christopher D. Sogge
Creator
Author
Subject
Language
eng
Summary
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, 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, 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
Member of
Cataloging source
UkCbUP
http://library.link/vocab/creatorDate
1960-
http://library.link/vocab/creatorName
Sogge, Christopher D.
Dewey number
515/.2433
Index
index present
LC call number
QA404
LC item number
.S64 1993
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Cambridge tracts in mathematics
Series volume
105
http://library.link/vocab/subjectName
  • Fourier series
  • Fourier integral operators
Label
Fourier integrals in classical analysis, Christopher D. Sogge
Link
https://doi.org/10.1017/CBO9780511530029
Instantiates
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
5. L[superscript p] Estimates of Eigenfunctions. 5.1. The Discrete L[superscript 2] Restriction Theorem. 5.2. Estimates for Riesz Means. 5.3. More General Multiplier Theorems -- 6. Fourier Integral Operators. 6.1. Lagrangian Distributions. 6.2. Regularity Properties. 6.3. Spherical Maximal Theorems: Take 1 -- 7. Local Smoothing of Fourier Integral Operators. 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems. 7.2. Local Smoothing in Higher Dimensions. 7.3. Spherical Maximal Theorems Revisited -- Appendix: Lagrangian Subspaces of T*R[superscript n]
Extent
1 online resource (x, 236 pages)
Form of item
online
Isbn
9780511530029
Isbn Type
(ebook)
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
digital, PDF file(s).
Specific material designation
remote
System control number
(UkCbUP)CR9780511530029
Label
Fourier integrals in classical analysis, Christopher D. Sogge
Link
https://doi.org/10.1017/CBO9780511530029
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
5. L[superscript p] Estimates of Eigenfunctions. 5.1. The Discrete L[superscript 2] Restriction Theorem. 5.2. Estimates for Riesz Means. 5.3. More General Multiplier Theorems -- 6. Fourier Integral Operators. 6.1. Lagrangian Distributions. 6.2. Regularity Properties. 6.3. Spherical Maximal Theorems: Take 1 -- 7. Local Smoothing of Fourier Integral Operators. 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems. 7.2. Local Smoothing in Higher Dimensions. 7.3. Spherical Maximal Theorems Revisited -- Appendix: Lagrangian Subspaces of T*R[superscript n]
Extent
1 online resource (x, 236 pages)
Form of item
online
Isbn
9780511530029
Isbn Type
(ebook)
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
digital, PDF file(s).
Specific material designation
remote
System control number
(UkCbUP)CR9780511530029

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