Shift-invariant Uniform Algebras on Groups (Hardcover, 2006 ed.)

The central subject of the book - the theory of shift-invariant algebras - is an outgrowth of the established theory of generalized analytic functions. Associated subalgebras of almost periodic functions of real variables and of bounded analytic functions on the unit disc are carried along within the general framework. In particular, it is shown that the algebra of almost periodic functions with spectrum in a semigroup of the reals does not have a half-plane-corona if and only if all non-negative semicharacters of the semigroup are monotone decreasing, or equivalently, if and only if the strong hull of the semigroup coincides with the positive half of its group envelope. Under the same conditions the corresponding subalgebra of bounded analytic functions on the disc has neither a half-plane-corona nor a disc-corona. There are given characterizations of semigroups such that classical theorems of complex analysis hold on the associated shift-invariant algebras. Bourgain algebras, orthogonal measures, and primary ideals of big disc algebras are described. The notion of a harmonic function is extended on compact abelian groups, and corresponding Fatou-type theorems are proven. Important classes of inductive limits of standard uniform algebras, including Blasche algebras, are introduced and studied. In particular, it is shown that algebras of hyper-analytic functions, associated with families of inner functions, do not have a big-disc-corona.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Monografie Matematyczne, 68
Release date:	May 2006
First published:	2006
Authors:	Suren A. Grigoryan • Toma V. Tonev
Dimensions:	244 x 170 x 21mm (L x W x T)
Format:	Hardcover
Pages:	287
Edition:	2006 ed.
ISBN-13:	978-3-7643-7606-2
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Promotions
LSN:	3-7643-7606-6
Barcode:	9783764376062

Is the information for this product incomplete, wrong or inappropriate? Let us know about it.

Does this product have an incorrect or missing image? Send us a new image.

Is this product missing categories? Add more categories.

Review This Product

No reviews yet - be the first to create one!