Almost automorphic solution Sums of commuting operators Analytic semigroup Uniform spectrum
Issue Date:
2004
Publisher:
Proceedings of the American Mathematical Society
Citation:
Volume 132, Issue 11, Page 3289-3298
Abstract:
This paper is concerned with the existence of almost automorphic mild solutions to equations of
the form (*) u??(t)=Au(t) + f(t), where A generates a holomorphic semigroup and f is an almost automorphic
function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of
the uniform spectrum of a function. By modifying the method of sums of commuting operators used in
previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for
the existence of almost automorphic mild solutions to (*) in terms of the imaginary spectrum of A and the
uniform spectrum of f.
