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Shift-invariant Uniform Algebras on Groups (Monografie Matematyczne) [Hardcover]

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Item description for Shift-invariant Uniform Algebras on Groups (Monografie Matematyczne) by Suren A. Grigoryan...

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 ofcomplex 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.



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Item Specifications...


Pages   284
Est. Packaging Dimensions:   Length: 9.1" Width: 6.5" Height: 0.8"
Weight:   1.45 lbs.
Binding  Hardcover
Release Date   Jun 30, 2006
Publisher   Birkhäuser Basel
ISBN  3764376066  
ISBN13  9783764376062  


Availability  93 units.
Availability accurate as of May 24, 2017 06:03.
Usually ships within one to two business days from La Vergne, TN.
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Product Categories

1Books > Subjects > Professional & Technical > Professional Science > Mathematics > Mathematical Analysis
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Functional Analysis
3Books > Subjects > Science > General
4Books > Subjects > Science > Mathematics > General
5Books > Subjects > Science > Mathematics > Mathematical Analysis
6Books > Subjects > Science > Mathematics > Pure Mathematics > Functional Analysis



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