Fourier Analysis and Convexity

Luca Brandolini, Leonardo Colzani, Alex Iosevich, Giancarlo Travaglini (Herausgeber)

Buch | Hardcover

268 Seiten

2004
Birkhauser Boston Inc (Verlag)
978-0-8176-3263-2 (ISBN)

Artikel merken

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 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.

Lattice Point Problems: Crossroads of Number Theory, Probability Theory and Fourier Analysis.- Totally Geodesic Radon Transform of LP-Functions on Real Hyperbolic Space.- Fourier Techniques in the Theory of Irregularities of Point Distribution.- Spectral Structure of Sets of Integers.- 100 Years of Fourier Series and Spherical Harmonics in Convexity.- Fourier Analytic Methods in the Study of Projections and Sections of Convex Bodies.- The Study of Translational Tiling with Fourier Analysis.- Discrete Maximal Functions and Ergodic Theorems Related to Polynomials.- What Is It Possible to Say About an Asymptotic of the Fourier Transform of the Characteristic Function of a Two-dimensional Convex Body with Nonsmooth Boundary?.- SomeRecent Progress on the Restriction Conjecture.- Average Decayof the Fourier Transform.

Erscheint lt. Verlag	6.8.2004
Reihe/Serie	Applied and Numerical Harmonic Analysis
Zusatzinfo	IX, 268 p.
Verlagsort	Secaucus
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8176-3263-8 / 0817632638
ISBN-13	978-0-8176-3263-2 / 9780817632632
Zustand	Neuware