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Bezig met laden... Lectures on harmonic analysis (2003)door Thomas H. Wolff, Izabella Aba, Carol Shubin
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This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book. Geen bibliotheekbeschrijvingen gevonden. |
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Google Books — Bezig met laden... GenresDewey Decimale Classificatie (DDC)515.2433Natural sciences and mathematics Mathematics Analysis General aspectsLC-classificatieWaarderingGemiddelde: Geen beoordelingen.Ben jij dit?Word een LibraryThing Auteur. |