Fourier Analysis in Convex Geometry is popular PDF and ePub book, written by Alexander Koldobsky in 2014-11-12, it is a fantastic choice for those who relish reading online the Uncategoriezed genre. Let's immerse ourselves in this engaging Uncategoriezed book by exploring the summary and details provided below. Remember, Fourier Analysis in Convex Geometry can be Read Online from any device for your convenience.
Fourier Analysis in Convex Geometry Book PDF Summary
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.
Detail Book of Fourier Analysis in Convex Geometry PDF
- Author : Alexander Koldobsky
- Release : 12 November 2014
- Publisher : American Mathematical Soc.
- ISBN : 9781470419523
- Genre : Uncategoriezed
- Total Page : 170 pages
- Language : English
- PDF File Size : 13,6 Mb
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