Suren A. Grigoryan, Toma V. Tonev

Shift-invariant Uniform Algebras on Groups (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Basel
• Seitenzahl: 287
• Erscheinungstermin: 8. August 2006
• Englisch
• ISBN-13: 9783764376055
• Artikelnr.: 37398136

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

"...this book will be useful for a wide range of analysts: the first chapters introduce basic tools of classical analysis (harmonic functions, almost periodic functions), of uniform algebras, of abstract harmonic analysis, and will be useful for beginning graduate students; the more advanced parts will interest research mathematicians and graduate students." -- Zentralblatt MATH