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A.Böttcher : On the Corona Theorem for Almost Periodic Functions

A.Böttcher : On the Corona Theorem for Almost Periodic Functions

Author(s) :
A.Böttcher
Title :
On the Corona Theorem for Almost Periodic Functions
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-8, 1998
Mathematics Subject Classification :
46J15 [ Banach algebras of differentiable functions ]
30H05 [ Spaces and algebras of analytic functions ]
42A75 [ Periodic functions and generalizations ]
43A60 [ Almost periodic functions on groups, etc. ]
47A68 [ Factorization theory of linear operators ]
Abstract :
Let AP_Sigma^+(R^n) denode the Banach algebra of all continuous allmost periodic functions on R^n whose Bohr-Fourier spectrum is contained in an additive semi-group Sigma p[0,infinity)^n . We show that the maximal ideal space of AP_Sigma^+(R^n) may have a nonempty corona and we characterize all Sigma for which the corona is empty. Analogous results are established for algebras of almost periodic functions with absolutely convergent Fourier series.
Keywords :
Corona Theorem, Almost Periodic Functions, Banach algebra
Language :
english
Publication time :
4/1998