Grigoryan / Tonev Shift-invariant Uniform Algebras on Groups

1. Auflage 2006
ISBN: 978-3-7643-7605-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 287 Seiten, Web PDF

Reihe: Mathematics and Statistics

The central subject of this book - the theory of shift-invariant algebras - is an outgrowth of the established theory of generalized analytic functions. This general framework carries along associated subalgebras of almost periodic functions of real variables and of bounded analytic functions on the unit disc. The text describes Bourgain algebras, orthogonal measures, and primary ideals of big disc algebras. The notion of a harmonic function is extended on compact abelian groups, and corresponding Fatou-type theorems are proven. Finally, the book introduces and studies classes of inductive limits of standard uniform algebras, including Blasche algebras. This is the first monograph devoted entirely to the topic.

Zielgruppe

Research

Autoren/Hrsg.

Grigoryan, Suren A.

Tonev, Toma V.

Inhaltsverzeichnis

Banach algebras and uniform algebras.- Three classical families of functions.- Groups and semigroups.- Shift-invariant algebras on compact groups.- Extension of semicharacters and additive weights.- G-disc algebras.- Harmonicity on groups and G-discs.- Shift-invariant algebras and inductive limit algebras on groups.