Contents:
Articles Cited by. Mathematica 38 1 , Integral Equations and Operator Theory 61 4 , , Proceedings of the American Mathematical Society 7 , , Bulletin of the London Mathematical Society 25 1 , , Illinois Journal of Mathematics 46 4 , , Canadian Journal of Mathematics 58 3 , , Illinois Journal of Mathematics 46 3 , , The Journal of Geometric Analysis 29 2 , , Department of Mathematics, University of Crete , Computational Methods and Function Theory 13 1 , , Bulletin of the London Mathematical Society 28 1 , , Journal of the London Mathematical Society 2 2 , , Articles 1—20 Show more.
Help Privacy Terms. Semigroups of composition operators and integral operators in spaces of analytic functions. Continuity of the operator of best uniform approximation by bounded analytic functions M Papadimitrakis Bulletin of the London Mathematical Society 25 1 , , A class of non-convex polytopes that admit no orthonormal basis of exponentials MN Kolountzakis, M Papadimitrakis Illinois Journal of Mathematics 46 4 , , Hausdorff and quasi-Hausdorff matrices on spaces of analytic functions P Galanopoulos, M Papadimitrakis Canadian Journal of Mathematics 58 3 , , On convexity of level curves of harmonic functions in the hyperbolic plane M Papadimitrakis Proc.
Soc 3 , , Condenser capacity under multivalent holomorphic functions M Papadimitrakis, S Pouliasis Computational Methods and Function Theory 13 1 , , Embed Size px x x x x D'Attellis anti E. Peters, J. Bates, G. Munger, andJ. A Prochazka, J. Uhlii', P. Rayner, andN. Bi andY. Brandolini, L.
Colzani, A losevich, andG. Fourier analysis. Convex geometry. Discrete geometry. Brandolini, Luca, II.
AII rights reserved. Use in connection with any form of information stora-ge and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to property rights.
In Hurwitz proved the isoperimetric inequality using Fourier series. It quicklybecame clear that this approach was not just a curiosity, but rather a fundamental ideawith far-reaching consequences and applications in geometry, analysis, and numbertheory.
During the last century the relationship between Fourier analysis and otherdisciplines has been systematically explored by many researchers resulting in impor-tant advances in these areas of study. One hundred years after the seminal paper by Hurwitz , a conference and sev-eral short courses dedicated to Fourier analysis, convex geometry, and related topicswere held at the Universita di Milano-Bicocca.
This conference was much more thana collection of long and short lectures: an important aspect of the meeting was the in-teraction among the speaker s and other participants. This interaction bore fruit in theform of joint publications and ever increasing movement towards interdisciplinaryconnections within mathematics. An outgrowth of the Milano conference, this volume contain s mainly exposi -tory or semi-expository invited chapters written by experts in their respective fields.
The chapters can arguably be broken up into three categorie s: number theory, latticepoints , and irregularities of distribution, represented by the contributions of Beck,Chen, and Green; interaction between Fourier analysis and convexity, represented bythe contributions of Groemer, Koldobsky, Ryabogin and Zvavitch, Podkorytov, andTravaglini; and interaction among Fourier analysis , geometric measure theory, andcombinatorics, represented by the contributions of Berenstein and Rubin, Kolountza-kis, Magyar, and Tao.
Although the chapters, and lectures on which they are based, were written in-dependently, there is a large number of common themes and connections amongthem. For example, the Fourier analytic approach to convex geometry is beautifullydescribed in an historical context in Groemer's chapter and echoed and developedby Koldobsky, Ryabogin and Zvavitch , and Berenstein and Rubin.
Editors: Brandolini, L., Colzani, L., Iosevich, A., Travaglini, G. (Eds.) 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. Request PDF on ResearchGate | Fourier Analysis and Convexity | Over the course of the last century, the systematic exploration of the relationship between .
The chapters byPodkorytov and Travaglini reverse the arrow of application by utilizing convex ge-ometric principles to establish Fourier analytic estimates, which in turn are used toprove results in geometric number theory. Common themes abound in the chaptersof Beck, Chen, Kolountzaki s, Magyar, even though the problem s discussed are not. We firmly believe that the commonthemes and con-nections implicit in the chapters were strengthened and refined by the discussionsand interactions that took place duringthe conference. Furthermore, the connectionsinherentin these chaptersare often deeperand moresurprisingthanone might think.
For example, Tao's chapter on restriction theory and Green's chapter on spectralproperties of subsets of the integers are not obviously related; nevertheless, it wasprecisely the interaction between these two fields of study that was an importantfactor in a number of spectacularbreakthroughs by Green and Tao in the study ofarithmeticprogressions and related problems. Our hope is that readers will appreciate this book as a testament to the powerof interdependence among different areas of mathematics, and not simply as a col-lection of interesting articlesby excellentmathematicians.
Webelievethat the bookwill be quite useful to graduate students and researchers in harmonicanalysis, con-vex geometry, functional analysis, number theory, computer science, and geometriccombinatorial analysis, who wish to learn more aboutproblems whereFourieranal-ysis is used to encodethe essenceof a mathematical problemin a naturalandelegantway.
We wish to thank John Benedetto, editor of the Applied and Numerical Har-monicAnalysis book series, for his encouragement and support. We also would liketo expressour sincere thanks to TomGrasso of Birkhauserfor his care and patience. Berenstein and Boris Rubin. Koldobsky, D. Ryabogin, and Artem Zvavitch.