| Edition |
Second edition. |
| Description |
1 online resource (xiv, 334 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Cambridge tracts in mathematics ; 210
|
|
Cambridge tracts in mathematics ; 210.
|
| 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. |
|
This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Background -- Stationary phase -- Non-homogeneous oscillatory integral operators -- Pseudo-differential operators -- The half-wave operator and functions of pseudo-differential operators -- Lp estimates of eigenfunctions -- Fourier integral operators -- Propagation of singularities and refined estimates -- Local smoothing of Fourier integral operators -- Kakeya-type maximal operators. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Fourier series.
|
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Fourier series. |
|
Fourier integral operators.
|
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Fourier integral operators. |
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Fourier analysis.
|
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MATHEMATICS -- Calculus. |
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Fourier analysis. |
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MATHEMATICS -- Mathematical Analysis. |
| Other Form: |
Print version record: Sogge, Christopher D. (Christopher Donald), 1960- Fourier integrals in classical analysis. Second edition. Cambridge : Cambridge University Press, 2017 9781107120075 (DLC) 2017004380 (OCoLC)971248650 |
| ISBN |
9781108234733 (electronic book) |
|
1108234739 (electronic book) |
|
9781316341186 |
|
1316341186 |
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9781107120075 (hardcover ; alkaline paper) |
|
1107120071 (hardcover ; alkaline paper) |
|
