Fourier Analysis and Hausdorff Dimension/
Mattila, Pertti
Fourier Analysis and Hausdorff Dimension/ [by] Pretti Mattila - Cambridge: Cambridge University Press, c2015 - xiii, 440 p. ; 24 cm. - Cambridge studies in advanced mathematics; 150 .
Includes bibliogrpahical references andb 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."--Back cover.
9781107107359 (hbk.): UKP 57.99 = MATHEMATICS
Fourier transformations.
Measure theory
Mathematical analysis.
Mathematics
515.2433 / MAT/F
Fourier Analysis and Hausdorff Dimension/ [by] Pretti Mattila - Cambridge: Cambridge University Press, c2015 - xiii, 440 p. ; 24 cm. - Cambridge studies in advanced mathematics; 150 .
Includes bibliogrpahical references andb 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."--Back cover.
9781107107359 (hbk.): UKP 57.99 = MATHEMATICS
Fourier transformations.
Measure theory
Mathematical analysis.
Mathematics
515.2433 / MAT/F
