Linear Time-Varying Systems With Almost-Periodic Kernels

The theory of almost periodic functions was first developed by the Dan-ish mathematician H.Bohr during 1925-1926.Soon after,there are further researcheson Bohr's theory,these include theory of harmonic analysis on Banach spaces in-troduced by S.Bochner in 1933.Then H.Weyl,A.Besicovitch,J.Favard,J.Von Neu-mann,V.V.Stepanov,N.N.Bogolyubo did further researches of the theory of stabil-ity,dynamics systems,which consummated the almost periodic function's theory.In developing the theory of the almost periodic type functions,a main feature isthat the scope is expanding:From Almost periodic function,Uniform almost periodicfunction,Asymptotically almost periodic function,Weakly almost periodic function toPseudo almost periodic function which was proposed by Professor Zhang in 1992.Ev-ery extension consumedly enlarges the application of the almost periodic functionaltheory.In the same,in the development of the theory of the almost periodic sequence,the scope is also expanding .To connect the almost periodic sequence with the systemand investigate the properties is the most important part in this paper.Then it is nessaryto introduce the concept of almost periodic system,which is a special time-varyingsystem.We know that time-varying system is a system which is more complicatedthan time-invariant system,so it is difficulty to talk over.But it is easier to investigatethe almost periodic system,so it is very important.In this paper,in allusion to above-motioned situations,two aspects of concrete work are done to almost periodic systemand the Pseudo almost periodic function.1 The properties of time-varying system and almost periodic system are dis-cussedThis paper discussed the new properties of almost periodic system,which is notpossessed in normal time-varying system.This paper also talk over some properties ofthe almost periodic functions which have been studied by predecessors.Here,we ex-tend them to the type of almost periodic functions,which will consummate the almostperiodic functions.2 And the properties of the Windowed fourier transform of Pseudo almost peri-odic function is investigated...