Fourier Analysis and Hausdorff Dimension
Jul. 2015 · Cambridge Studies in Advanced Mathematics Boek 150 · Cambridge University Press
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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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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.
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