Lynn H. Loomis

Introduction to Abstract Harmonic Analysis (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This classic monograph is the work of a prominent contributor to the field of harmonic analysis. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. Prerequisites include a knowledge of the concepts of elementary modern algebra and of metric space topology.
The first three chapters feature concise, self-contained treatments of measure theory, general topology, and Banach space theory that will assist students in their grasp of subsequent material. An in-depth exposition of Banach algebra follows, along with examinations of the Haar integral and the deduction of the standard theory of harmonic analysis on locally compact Abelian groups and compact groups. Additional topics include positive definite functions and the generalized Plancherel theorem, the Wiener Tauberian theorem and the Pontriagin duality theorem, representation theory, and the theory of almost periodic functions.

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Produktdetails

• Verlag: Dover Publications
• Seitenzahl: 208
• Erscheinungstermin: 11. April 2013
• Englisch
• ISBN-13: 9780486282312
• Artikelnr.: 39550084

Inhaltsangabe

I. Topology II. The Banach Spaces III. Integration IV. Banach Algebras V.
Some Special Banach Algebras VI. The Haar Integral VII. Locally Compact
Abelian Groups VIII. Compact Groups and Almost Periodic Functions IX. Some
Further Developments Bibliography Index