Accession Number : ADA139312

Title :   On the Almost Periodicity of the Solutions of an Integrodifferential Equation.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Staffans,O J

PDF Url : ADA139312

Report Date : Feb 1984

Pagination or Media Count : 25

Abstract : This paper discusses the almost periodicity of bounded solutions of the integrodifferential equation x' + micron * x = f. Here x and f map R into C sub n, the prime denotes differentiation, micron is an n by n matrix valued finite measure on R, and f is either an almost periodic distribution, or an almost periodic function in the sense of Bohr, Stephanoff, Weyl or Besicovitch. In the first three cases the author gives a simple sufficient condition (countability of the set where the characteristic function of the kernel is not invertible) for bounded solutions to be almost periodic. This condition is not longer sufficient in the last two cases, as is shown with a simple counterexample. (Author)

Descriptors :   *Linear differential equations, *Integral equations, *Solutions(General), Periodic functions, Theorems, Fourier series, Kernel functions, Convolution

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE