Further Extensions of the Choquet-Deny and Deny Theorems with Applications in Characterization Theory.
Technical rept. for period ending Aug 87,
PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS
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This paper aims at extending the Davies-Shanbhag 1987 result to situations covering the problems considered by Schimizu 1978, 1980, Gu and Lau 1984 and Ramachandran et al 1987. Section 2, gives the results when H is bounded and micron is replaced by a certain bounded signed measure subsuming the specialized versions of the results given earlier by Shimizu 1978 and Ramchandran et al 1987 these turn out to be also extended versions of the Choquet-Deny theorem. Section 3 considers an extension of the Davies-Shanbhag result for the case of two simultaneous equations yielding the results of Ramachandran et al 1987 and those arrived at by some of the authors as special cases. Section 4 obtains extended versions of the results involving error terms given earlier by Shimizu 1980 and Gu and Lau 1984, and finally in Section 5, we discuss some applications. Keywords Integrated cauchy functional equations.
- Numerical Mathematics