Fourier Analysis and Hausdorff Dimension
eBook - PDF

Fourier Analysis and Hausdorff Dimension

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Fourier Analysis and Hausdorff Dimension

About this book

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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Yes, you can access Fourier Analysis and Hausdorff Dimension by Pertti Mattila in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half title
  3. Series
  4. Title
  5. Copyright
  6. Dedication
  7. Contents
  8. Preface
  9. Acknowledgements
  10. 1 Introduction
  11. Part I Preliminaries and some simpler applications of the Fourier transform
  12. Part II Specific constructions
  13. Part III Deeper applications of the Fourier transform
  14. Part IV Fourier restriction and Kakeyatype problems
  15. References
  16. Index of basic notation
  17. Author index
  18. Subject index