Accession Number : AD0697644

Title :   CRITICAL LINEAR DIFFERENCE EQUATIONS: A STUDY IN PATHOLOGY,

Corporate Author : IOWA UNIV IOWA CITY DEPT OF MATHEMATICS

Personal Author(s) : Hurt,James J. ; Schaeffer,Anthony J.

Report Date : JUN 1969

Pagination or Media Count : 19

Abstract : The paper discusses the structure of solutions of the linear scaler difference equation x(t + h) = x(t) + f(t), and in part its relationship to the differential equation x dot (t) = f(t). It is shown that the structure of solutions of the difference equation is critically dependent on h. For example, given f periodic, there is a dense set of h's for which there is not even a generalized periodic solution, no matter how smooth f is. Conditions on f for boundedness and uniform continuity of solutions are obtained and an example is presented to show that if f is almost periodic and the solution is bounded, the solution need not be almost periodic. (Author)

Descriptors :   (*DIFFERENCE EQUATIONS, HARMONIC ANALYSIS), DIFFERENTIAL EQUATIONS, TRANSCENDENTAL FUNCTIONS, FOURIER ANALYSIS, SERIES(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE