A First Course in Harmonic Analysis

2. Auflage 2005
ISBN: 978-0-387-22837-2
Verlag: Springer

Buch, Englisch, 192 Seiten, Format (B × H): 154 mm x 233 mm, Gewicht: 354 g

Reihe: Universitext

Affordable softcover second edition of bestselling title (over 1000 copies sold of previous edition)

A primer in harmonic analysis on the undergraduate level

Gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory.

Entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology.

Almost all proofs are given in full and all central concepts are presented clearly.

Provides an introduction to Fourier analysis, leading up to the Poisson Summation Formula.

Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups.

Introduces the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Deitmar, Anton

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe

Inhaltsverzeichnis

Fourier Analysis.- Fourier Series.- Hilbert Spaces.- The Fourier Transform.- Distributions.- LCA Groups.- Finite Abelian Groups.- LCA Groups.- The Dual Group.- Plancherel Theorem.- Noncommutative Groups.- Matrix Groups.- The Representations of SU(2).- The Peter-Weyl Theorem.- The Heisenberg Group.

Über Autor(innen)

Professor Deitmar holds a Chair in Pure Mathematics at the University of Exeter, U.K. He is a former Heisenberg fellow and was awarded the main prize of the Japanese Association of Mathematical Sciences in 1998. In his leisure time he enjoys hiking in the mountains and practicing Aikido.