Displaying similar documents to “Representations and Positive Definite Functions on Hypergroups”

On convolution operators with small support which are far from being convolution by a bounded measure

Edmond Granirer (1994)

Colloquium Mathematicae

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Let C V p ( F ) be the left convolution operators on L p ( G ) with support included in F and M p ( F ) denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that C V p ( F ) , C V p ( F ) / M p ( F ) and C V p ( F ) / W are as big as they can be, namely have l as a quotient, where the ergodic space W contains, and at times is very big relative to M p ( F ) . Other subspaces of C V p ( F ) are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

Decomposition and disintegration of positive definite kernels on convex *-semigroups

Jan Stochel (1992)

Annales Polonici Mathematici

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The paper deals with operator-valued positive definite kernels on a convex *-semigroup whose Kolmogorov-Aronszajn type factorizations induce *-semigroups of bounded shift operators. Any such kernel Φ has a canonical decomposition into a degenerate and a nondegenerate part. In case is commutative, Φ can be disintegrated with respect to some tight positive operator-valued measure defined on the characters of if and only if Φ is nondegenerate. It is proved that a representing measure of...

Second order evolution equations with parameter

Jan Bochenek, Teresa Winiarska (1994)

Annales Polonici Mathematici

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We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter h Ω m . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.