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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Number Theory, Fourier Analysis and Geometric Discrepancy (Paperback)
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Number Theory, Fourier Analysis and Geometric Discrepancy (Paperback)
Series: London Mathematical Society Student Texts
Expected to ship within 12 - 17 working days
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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 self-contained 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 Koksma
Hlawka 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, one-sided
trigonometric approximation, the Poisson summation formula,
exponential sums, decay of Fourier transforms, and Bessel
functions."
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