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
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Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz’s proof of the isoperimetric inequality using Fourier series. This unified, self-contained volume is dedicated to Fourier analysis, convex geometry, and related topics. Specific topics covered include: * the geometric properties of convex bodies * the study of Radon transforms * the geometry of numbers * the study of translational tilings using Fourier analysis * irregularities in distributions * Lattice point problems examined in the context of number theory, probability theory, and Fourier analysis * restriction problems for the Fourier transform The book presents both a broad overview of Fourier analysis and convexity as well as an intricate look at applications in some specific settings; it will be useful to graduate students and researchers in harmonic analysis, convex geometry, functional analysis, number theory, computer science, and combinatorial analysis. A wide audience will benefit from the careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way. Contributors: J. Beck, C. Berenstein, W.W.L. Chen, B. Green, H. Groemer, A. Koldobsky, M. Kolountzakis, A. Magyar, A.N. Podkorytov, B. Rubin, D. Ryabogin, T. Tao, G. Travaglini, A. Zvavitch
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Key Phrases - Statistically Improbable Phrases (SIPs):
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wave packet decomposition, notched cube, coset ring, extremal sections, restriction conjecture, bilinear estimates, maximal ergodic theorem, restriction estimates, integral row, lattice tilings, common tile, pointwise ergodic theorem, intersection bodies, symmetric convex bodies, symmetric convex body, tilted rectangles, lattice point problem, intersection body, maximal theorem, quadratic irrationals, bounded density, tiling problem, maximal function, maximal operators, surface area measure Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Duke Math, Diophantine Lemma, Cambridge University Press, Department of Mathematics, London Math, Acta Arith, Acta Math, Casadio Tarabusi, Annals of Math, Pure Math, Academic Press, Chord Lemma, Reine Angew, Revista Mat, The Brunn-Minkowski Theory New!
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wave packet decomposition, notched cube, coset ring, extremal sections, restriction conjecture, bilinear estimates, maximal ergodic theorem, restriction estimates, integral row, lattice tilings, common tile, pointwise ergodic theorem, intersection bodies, symmetric convex bodies, symmetric convex body, tilted rectangles, lattice point problem, intersection body, maximal theorem, quadratic irrationals, bounded density, tiling problem, maximal function, maximal operators, surface area measure Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Duke Math, Diophantine Lemma, Cambridge University Press, Department of Mathematics, London Math, Acta Arith, Acta Math, Casadio Tarabusi, Annals of Math, Pure Math, Academic Press, Chord Lemma, Reine Angew, Revista Mat, The Brunn-Minkowski Theory New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 45
books:
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3
books
cite this book:
- Geometric Tomography (Encyclopedia of Mathematics and its Applications) by Richard J. Gardner on page 56, page 118, and page 129
- Convex Bodies: The Brunn-Minkowski Theory (Encyclopedia of Mathematics and its Applications) by Rolf Schneider on page 57, page 118, and page 130
- Geometric Applications of Fourier Series and Spherical Harmonics (Encyclopedia of Mathematics and its Applications) by Helmut Groemer on page 56, and page 118
- Irregularities of Distribution (Cambridge Tracts in Mathematics) by Jozsef Beck on page 34, and Back Matter
- Harmonic Analysis by Elias M. Stein on page 242, and Back Matter
See all 45 books this book cites
- Multiscale Potential Theory by Willi Freeden in Front Matter
- Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations (Applied and Numerical Harmonic Analysis) by Ovidiu Calin on page
- Time Frequency and Time-Scale Methodes by Jeffrey A. Hogan in Back Matter
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