Fourier analysis and Hausdorff dimension / (Record no. 651944)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03555nam a22004218i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9781316227619 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20250930143539.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 141020s2015||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781316227619 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781107107359 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA403.5 |
| Item number | .M38 2015 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.2/433 |
| Edition information | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Mattila, Pertti, |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Fourier analysis and Hausdorff dimension / |
| Statement of responsibility, etc. | Pertti Mattila. |
| 246 3# - VARYING FORM OF TITLE | |
| Title proper/short title | Fourier Analysis & Hausdorff Dimension |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cambridge : |
| Name of producer, publisher, distributor, manufacturer | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2015. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xiv, 440 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Cambridge studies in advanced mathematics ; |
| Volume/sequential designation | 150 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Preface -- Acknowledgements -- Introduction -- Part 1. Preliminaries and some simpler applications of the Fourier transform. Measure theoretic preliminaries -- Fourier transforms -- Hausdorff dimension of projections and distance sets -- Exceptional projections and Sobolev dimension -- Slices of measures and intersections with planes -- Intersections of general sets and measures -- Part 2. Specific constructions. Cantor measures -- Bernoulli convolutions -- Projections of the four-corner Cantor set -- Besicovitch sets -- Brownian motion -- Riesz products -- Oscillatory integrals (stationary phase) and surface measures -- Part 3. Deeper applications of the Fourier transform. Spherical averages and distance sets -- Proof of the Wolff-Erdoğan Theorem -- Sobolev spaces, Schrödinger equation and spherical averages -- Generalized projections of Peres and Schlag -- Part 4. Fourier restriction and Kakeya type problems. Restriction problems -- Stationary phase and restriction -- Fourier multipliers -- Kakeya problems -- Dimension of Besicovitch sets and Kakeya maximal inequalities -- (n, k) Besicovitch sets -- Bilinear restriction. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Fourier transformations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Measure theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Mathematical analysis. |
| 9 (RLIN) | 60397 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| International Standard Book Number | 9781107107359 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Cambridge studies in advanced mathematics ; |
| Volume/sequential designation | 150. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9781316227619">https://doi.org/10.1017/CBO9781316227619</a> |
| 907 ## - LOCAL DATA ELEMENT G, LDG (RLIN) | |
| a | .b16846011 |
| b | 2020-12-22 |
| c | 2020-12-22 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Suppress in OPAC | No |
| 998 ## - LOCAL CONTROL INFORMATION (RLIN) | |
| Library | |
| Operator's initials, OID (RLIN) | 2020-12-22 |
| Cataloger's initials, CIN (RLIN) | m |
| Material Type (Sierra) | Printed Books |
| Language | English |
| Country | |
| -- | 0 |
| -- | .b16846011 |
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