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Author : Keith M. Ball
Release : 1999-01-28
Genre : Mathematics
Kind : eBook
Book Rating : 590/5 ( reviews)
Book Synopsis Convex Geometric Analysis by : Keith M. Ball
Download or read book Convex Geometric Analysis written by Keith M. Ball. This book was released on 1999-01-28. Available in PDF, EPUB and Kindle. Book excerpt: Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999.
Author : Daniel Hug
Release : 2020-08-27
Genre : Mathematics
Kind : eBook
Book Rating : 809/5 ( reviews)
Book Synopsis Lectures on Convex Geometry by : Daniel Hug
Download or read book Lectures on Convex Geometry written by Daniel Hug. This book was released on 2020-08-27. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Author : Steven G. Krantz
Release : 2014-10-20
Genre : Mathematics
Kind : eBook
Book Rating : 38X/5 ( reviews)
Book Synopsis Convex Analysis by : Steven G. Krantz
Download or read book Convex Analysis written by Steven G. Krantz. This book was released on 2014-10-20. Available in PDF, EPUB and Kindle. Book excerpt: Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and other parts of mathematics.Convex Analysis introduces
Author : Alexander Koldobsky
Release : 2014-11-12
Genre : Mathematics
Kind : eBook
Book Rating : 521/5 ( reviews)
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.
Author : Ilya J. Bakelman
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 816/5 ( reviews)
Book Synopsis Convex Analysis and Nonlinear Geometric Elliptic Equations by : Ilya J. Bakelman
Download or read book Convex Analysis and Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.
