Share

Fourier Analysis in Convex Geometry

2014-11-12 Mathematics
Download Fourier Analysis in Convex Geometry PDF Online Free

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

GET EBOOK


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.

Applications of the Fourier Transform to Convex Geometry

2006 Convex geometry
Download Applications of the Fourier Transform to Convex Geometry PDF Online Free

Author :
Release : 2006
Genre : Convex geometry
Kind : eBook
Book Rating : /5 ( reviews)

GET EBOOK


Book Synopsis Applications of the Fourier Transform to Convex Geometry by : Vladyslav Yaskin

Download or read book Applications of the Fourier Transform to Convex Geometry written by Vladyslav Yaskin. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: The thesis is devoted to the study of various problems arising from Convex Geometry and Geometric Functional Analysis using tools of Fourier Analysis. In chapters two through four we consider the Busemann-Petty problem and its different modifications and generalizations. We solve the Busemann-Petty problem in hyperbolic and spherical spaces, and the lower dimensional Busemann-Petty problem in the hyperbolic space. In the Euclidean space we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions. In chapter five we introduce the notion of embedding of a normed space in L0, investigate the geometry of such spaces and prove results confirming the place of L0 in the scale of L [subscript p] spaces. Chapter six is concerned with the study L [subscript p]-centroid bodies associated to symmetric convex bodies and generalization of some known results of Lutwak and Grinberg, Zhang to the case [minus] 1 [less than] p [less than] 1. In chapter seven we discuss Khinchin type inequalities and the slicing problem. We obtain a version of such inequalities for p [greater than] [minus] 2 and as a consequence we prove the slicing problem for the unit balls of spaces that embed in L[subscript] p, p [greater than] [minus] 2.

Fourier Analysis and Convexity

2011-04-27 Mathematics
Download Fourier Analysis and Convexity PDF Online Free

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

GET EBOOK


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

The Interface Between Convex Geometry and Harmonic Analysis

2008 Mathematics
Download The Interface Between Convex Geometry and Harmonic Analysis PDF Online Free

Author :
Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 564/5 ( reviews)

GET EBOOK


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 2008. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the modern results of convex geometry using harmonic analysis outlines the development of Fourier analysis and how its methods are used to solve geometric problems. The book includes new results since a previous book from the author in 2005. The material is presented in lecture format, with the first section of each lecture offering an accessible snapshot for novice readers.

Geometric Applications of Fourier Series and Spherical Harmonics

1996-09-13 Mathematics
Download Geometric Applications of Fourier Series and Spherical Harmonics PDF Online Free

Author :
Release : 1996-09-13
Genre : Mathematics
Kind : eBook
Book Rating : 187/5 ( reviews)

GET EBOOK


Book Synopsis Geometric Applications of Fourier Series and Spherical Harmonics by : H. Groemer

Download or read book Geometric Applications of Fourier Series and Spherical Harmonics written by H. Groemer. This book was released on 1996-09-13. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

You may also like...