The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a selfcontained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the KoksmaHlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, onesided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions.
About Giancarlo Travaglini
Giancarlo Travaglini is Professor of Mathematics at the University of MilanoBicocca. He is the author of numerous research papers and several books in the areas of abstract harmonic analysis, Fourier analysis and discrepancy theory. He is a member of the Unione Matematica Italiana and the American Mathematical Society. His current mathematical interests include Fourier analysis, discrepancy theory, radon transforms and didactics of mathematics.Details Book
Author  :  Giancarlo Travaglini 
Publisher  :  Cambridge University Press 
Data Published  :  12 June 2014 
ISBN  :  1107044030 
EAN  :  9781107044036 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  252 pages 
Age +  :  18 years 
Language  :  English 
Rating  : 
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