Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Harmonic Analysis and Convexity PDF full book. Access full book title Harmonic Analysis and Convexity by Alexander Koldobsky. Download full books in PDF and EPUB format.
Author: Alexander Koldobsky Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110775433 Category : Mathematics Languages : en Pages : 608
Book Description
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.
Author: Alexander Koldobsky Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110775433 Category : Mathematics Languages : en Pages : 608
Book Description
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.
Author: Luca Brandolini Publisher: Springer Science & Business Media ISBN: 0817681728 Category : Mathematics Languages : en Pages : 268
Book Description
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
Author: Gabriele Bianchi Publisher: Springer ISBN: 3319718347 Category : Mathematics Languages : en Pages : 125
Book Description
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.
Author: Alexander Koldobsky Publisher: American Mathematical Soc. ISBN: 1470419521 Category : Mathematics Languages : en Pages : 178
Book Description
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.
Author: Alexander Koldobsky Publisher: American Mathematical Soc. ISBN: 9780821883358 Category : Mathematics Languages : en Pages : 128
Book Description
"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.
Author: Silouanos Brazitikos Publisher: American Mathematical Soc. ISBN: 1470414562 Category : Mathematics Languages : en Pages : 618
Book Description
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
Author: Gerrit van Dijk Publisher: Walter de Gruyter ISBN: 3110220199 Category : Mathematics Languages : en Pages : 234
Book Description
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Author: Carlos E. Kenig Publisher: American Mathematical Soc. ISBN: 1470461277 Category : Education Languages : en Pages : 345
Book Description
The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.
Author: J. Carmona Publisher: Springer ISBN: 3540351310 Category : Mathematics Languages : en Pages : 249
Book Description
Acoustics and the Performance of Music connects scientific understandings of acoustics with practical applications to musical performance. Of central importance are the tonal characteristics of musical instruments and the singing voice including detailed representations of directional characteristics. Furthermore, room acoustical concerns related to concert halls and opera houses are considered. Based on this, suggestions are made for musical performance. Included are seating arrangements within the orchestra and adaptations of performance techniques to the performance environment. In the presentation we dispense with complicated mathematical connections and deliberately aim for conceptual explanations accessible to musicians, particularly for conductors. The graphical representations of the directional dependence of sound radiation by musical instruments and the singing voice are unique. Since the first edition was published in 1978, this book has been completely revised and rewritten to include current research. This translation corresponds to the latest (fifth) German edition (2004), which has become a standard reference work for audio engineers and scientists. Acoustics and the Performance of Music addresses issues that are of interest to acousticians, orchestra performers and conductors, audio engineers, architects. Researchers and students of musical acoustics will also find this text valuable.
Author: Victor Havin Publisher: Springer Science & Business Media ISBN: 3642783775 Category : Mathematics Languages : en Pages : 547
Book Description
The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose).
Author: Alexander Koldobsky
Author: Alexander Koldobsky
Author: Luca Brandolini
Author: Gabriele Bianchi
Author: Alexander Koldobsky
Author: Alexander Koldobsky
Author: Silouanos Brazitikos
Author: Gerrit van Dijk
Author: Carlos E. Kenig
Author: J. Carmona
Author: Victor Havin