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Fourier integrals in classical analysis

Sogge, Christopher D. (1960-)

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Fourier integrals in classical analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fourier integrals in classical analysis/ Christopher D. Sogge.
Author:	Sogge, Christopher D.
Published:	Cambridge :Cambridge University Press, : 1993.,
Description:	x, 236 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	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].
Subject:	Fourier series. -
Online resource:	https://doi.org/10.1017/CBO9780511530029
ISBN:	9780511530029

Fourier integrals in classical analysis
Sogge, Christopher D.1960-

Fourier integrals in classical analysis[electronic resource] /Christopher D. Sogge. - Cambridge :Cambridge University Press,1993. - x, 236 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;105. - Cambridge tracts in mathematics ;105..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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].

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.

ISBN: 9780511530029Subjects--Topical Terms:

544165
Fourier series.

LC Class. No.: QA404 / .S64 1993

Dewey Class. No.: 515.2433

Fourier integrals in classical analysis
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040 $a UkCbUP $b eng $c UkCbUP $d GP
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050 4 $a QA404 $b .S64 1993
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100 1 $a Sogge, Christopher D. $q (Christopher Donald), $d 1960- $3 3470424
245 1 0 $a Fourier integrals in classical analysis $h [electronic resource] / $c Christopher D. Sogge.
260 $a Cambridge : $b Cambridge University Press, $c 1993.
300 $a x, 236 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 105
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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].
520 $a 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.
650 0 $a Fourier series. $3 544165
650 0 $a Fourier integral operators. $3 700325
830 0 $a Cambridge tracts in mathematics ; $v 105. $3 3470425
856 4 0 $u https://doi.org/10.1017/CBO9780511530029