Screen LibraryFourier analysis and Hausdorff dimension /
"During the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. The main topics concern applications of the...
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| Main Authors: | |
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| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge, United Kingdom : |
| Publication Dates: | 2015. |
| Literature type: | Book |
| Language: | English |
| Series: |
Cambridge studies in advanced mathematics ;
150 |
| Subjects: | |
| Summary: |
"During the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. The main topics concern applications of the Fourier transform to geometric problems involving Hausdorff dimension, such as Marstrand type projection theorems and Falconer's distance set problem, and the role of Hausdorff dimension in modern Fourier analysis, especially in Kakeya methods and Fourier restriction phenomena. The discussion includes |
| Carrier Form: | xiv, 440 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 416-433) and indexes. |
| ISBN: |
9781107107359 : 1107107350 |
| Index Number: | QA403 |
| CLC: | O174.22 |
| Call Number: | O174.22/M444 |
| Contents: | Preface -- Acknowledgements -- Introduction -- Part 1. Preliminaries and some simpler applications of the Fourier transform. Measure theoretic preliminaries -- Fourier transforms -- Hausdorff dimension of projections and distance sets -- Exceptional projections and Sobolev dimension -- Slices of measures and intersections with planes -- Intersections of general sets and measures -- Part 2. Specific constructions. Cantor measures -- Bernoulli convolutions -- Projections of the four-corner Cantor set -- Besicovitch sets -- Brownian motion -- Riesz products -- Oscillatory integrals (stationary |