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

Author(s) :

A.Böttcher

Title :

On the Corona Theorem for Almost Periodic Functions

Electronic source:

application/pdf

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