During the last century the relationship between Fourier analysis and other areas of mathematics has been systematically explored resulting in important advances in geometry, number theory, and analysis. The expository articles in this unified, self-contained volume explore those advances and connections. Specific topics covered included: geometric properties of convex bodies, Radon transforms, geometry of numbers, tilings, irregularities in distributions, and restriction problems for the Fourier transform. Graduate students and researchers in harmonic analysis, convex geometry, and functional analysis will benefit from the book's careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way.
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Research
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Illustrationen
Maße
Höhe: 242 mm
Breite: 165 mm
Dicke: 19 mm
Gewicht
ISBN-13
978-0-8176-3263-2 (9780817632632)
DOI
10.1007/978-0-8176-8172-2
Schweitzer Klassifikation
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.
