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Harmonic Analysis and Convexity

2023-07-24 Mathematics
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Release : 2023-07-24
Genre : Mathematics
Kind : eBook
Book Rating : 433/5 ( reviews)

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Book Synopsis Harmonic Analysis and Convexity by : Alexander Koldobsky

Download or read book Harmonic Analysis and Convexity written by Alexander Koldobsky. This book was released on 2023-07-24. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.

Fourier Analysis and Convexity

2011-04-27 Mathematics
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Release : 2011-04-27
Genre : Mathematics
Kind : eBook
Book Rating : 728/5 ( reviews)

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Book Synopsis Fourier Analysis and Convexity by : Luca Brandolini

Download or read book Fourier Analysis and Convexity written by Luca Brandolini. This book was released on 2011-04-27. Available in PDF, EPUB and Kindle. Book excerpt: Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances Presents new results and applications to diverse fields such as geometry, number theory, and analysis Contributors are leading experts in their respective fields Will be of interest to both pure and applied mathematicians

Analytic Aspects of Convexity

2018-02-28 Mathematics
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Release : 2018-02-28
Genre : Mathematics
Kind : eBook
Book Rating : 347/5 ( reviews)

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Book Synopsis Analytic Aspects of Convexity by : Gabriele Bianchi

Download or read book Analytic Aspects of Convexity written by Gabriele Bianchi. This book was released on 2018-02-28. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016. It offers a collection of selected articles, written by some of the world’s leading experts in the field of Convex Geometry, on recent developments in this area: theory of valuations; geometric inequalities; affine geometry; and curvature measures. The book will be of interest to a broad readership, from those involved in Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in Convex Geometry and its links to analysis.

Fourier Analysis in Convex Geometry

2014-11-12 Mathematics
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Release : 2014-11-12
Genre : Mathematics
Kind : eBook
Book Rating : 521/5 ( reviews)

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Book Synopsis Fourier Analysis in Convex Geometry by : Alexander Koldobsky

Download or read book Fourier Analysis in Convex Geometry written by Alexander Koldobsky. This book was released on 2014-11-12. Available in PDF, EPUB and Kindle. Book excerpt: The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the -dimensional volume of hyperplane sections of the -dimensional unit cube (it is for each ). Another is the Busemann-Petty problem: if and are two convex origin-symmetric -dimensional bodies and the -dimensional volume of each central hyperplane section of is less than the -dimensional volume of the corresponding section of , is it true that the -dimensional volume of is less than the volume of ? (The answer is positive for and negative for .) The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.

The Interface Between Convex Geometry and Harmonic Analysis

Mathematics
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Genre : Mathematics
Kind : eBook
Book Rating : 358/5 ( reviews)

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Book Synopsis The Interface Between Convex Geometry and Harmonic Analysis by : Alexander Koldobsky

Download or read book The Interface Between Convex Geometry and Harmonic Analysis written by Alexander Koldobsky. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: "The book is written in the form of lectures accessible to graduate students. This approach allows the reader to clearly see the main ideas behind the method, rather than to dwell on technical difficulties. The book also contains discussions of the most recent advances in the subject. The first section of each lecture is a snapshot of that lecture. By reading each of these sections first, novices can gain an overview of the subject, then return to the full text for more details."--BOOK JACKET.

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