FOURIER ANALYSIS AND HAUSDORFF DIMENSION by Pertti Mattila ( 9781107107359 )

Item Details

Title:

FOURIER ANALYSIS AND HAUSDORFF DIMENSION

By:

Pertti Mattila

Format:

Hardback

List price:

£73.00

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£65.70

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£7.30

ISBN 10:

1107107350

ISBN 13:

9781107107359

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Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

22 July, 2015

Series:

Cambridge Studies in Advanced Mathematics 150

Pages:

452

Description:

Modern text examining the interplay between measure theory and Fourier analysis.

Synopsis:

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 both classical results and recent developments in the area. The author emphasises partial results of important open problems, for example, Falconer's distance set conjecture, the Kakeya conjecture and the Fourier restriction conjecture. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.

Illustrations:

5 b/w illus.

Publication:

Imprint:

Cambridge University Press

Returns:

Returnable

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