Fourier Analysis and Hausdorff Dimension

Pertti Mattila (University of Helsinki)

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English

Cambridge University Press
23 July 2015

Mathematics; Calculus & mathematical analysis; Real analysis, real variables; Complex analysis, complex variables; Geometry

Series: Cambridge Studies in Advanced Mathematics

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.

By: Pertti Mattila (University of Helsinki)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 150
Dimensions: Height: 235mm, Width: 157mm, Spine: 29mm
Weight: 760g
ISBN: 9781107107359
ISBN 10: 1107107350
Series: Cambridge Studies in Advanced Mathematics
Pages: 452
Publication Date: 23 July 2015
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Pertti Mattila is Professor of Mathematics at the University of Helsinki and an expert in geometric measure theory. He has authored the book Geometry of Sets and Measures in Euclidean Spaces as well as more than 80 other scientific publications.

Reviews for Fourier Analysis and Hausdorff Dimension

'Mattila deserves kudos for having written an excellent text for the community of graduate students and research mathematicians with an analytic bent, one that exposes in considerable detail a particularly rich seam of mathematics at the interface between harmonic analysis and geometric measure theory in Euclidean space ... Libraries should be encouraged to buy their copies in haste.' Tushar Das, MAA Reviews