Fourier analysis and hausdorff dimension

By:

Mattila, Pertti

Series: Cambridge studies in advanced mathematics ; 150Publication details: Cambridge University Press, 2015. Cambridge:Description: xiv, 440 p. : ill. ; hb. ; 24 cmISBN:

9781107107359

Subject(s):

DDC classification:

515.2433 MAT

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 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.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	515.2433 MAT (Browse shelf(Opens below))	1	Available		030095

Formerly CIP.
Includes bibliographical references and index.

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.

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