Shift-invariant Uniform Algebras on Groups
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Beschreibung
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.
Novel approach and techniques leading to non-standard perspectives and unexpected properties of the classes of almost periodic functions of real variables and of bounded analytic functions on the unit disc First monograph devoted entirely to an outgrowth of the established theory of generalized analytic functions on compact groups Inclusion of subalgebras of the above functions with their own specifics
Autor*in
Suren A. Grigoryan
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Banach algebra Complex analysis algebra analytic function functional analysis
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"…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
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