Fourier analysis and Hausdorff dimension:
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 Fourie...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
|
| Series: | Cambridge studies in advanced mathematics
150 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBM01 UBR01 Volltext |
| 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 |
| Physical Description: | 1 Online-Ressource (xiv, 440 Seiten) |
| ISBN: | 9781316227619 |
| DOI: | 10.1017/CBO9781316227619 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9781316227619 |
| language | English |
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| spelling | Mattila, Pertti 1947- Verfasser (DE-588)1075782376 aut Fourier analysis and Hausdorff dimension Pertti Mattila, University of Helsinki Fourier analysis & Hausdorff dimension Cambridge Cambridge University Press 2015 1 Online-Ressource (xiv, 440 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 150 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 Fourier transformations Measure theory Mathematical analysis Hausdorff-Dimension (DE-588)4159234-7 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Hausdorff-Dimension (DE-588)4159234-7 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-1-107-10735-9 Cambridge studies in advanced mathematics 150 (DE-604)BV044781283 150 https://doi.org/10.1017/CBO9781316227619 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Mattila, Pertti 1947- Fourier analysis and Hausdorff dimension Cambridge studies in advanced mathematics Fourier transformations Measure theory Mathematical analysis Hausdorff-Dimension (DE-588)4159234-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4159234-7 (DE-588)4023453-8 |
| title | Fourier analysis and Hausdorff dimension |
| title_alt | Fourier analysis & Hausdorff dimension |
| title_auth | Fourier analysis and Hausdorff dimension |
| title_exact_search | Fourier analysis and Hausdorff dimension |
| title_full | Fourier analysis and Hausdorff dimension Pertti Mattila, University of Helsinki |
| title_fullStr | Fourier analysis and Hausdorff dimension Pertti Mattila, University of Helsinki |
| title_full_unstemmed | Fourier analysis and Hausdorff dimension Pertti Mattila, University of Helsinki |
| title_short | Fourier analysis and Hausdorff dimension |
| title_sort | fourier analysis and hausdorff dimension |
| topic | Fourier transformations Measure theory Mathematical analysis Hausdorff-Dimension (DE-588)4159234-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Fourier transformations Measure theory Mathematical analysis Hausdorff-Dimension Harmonische Analyse |
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