Displaying similar documents to “On extension of scalar valued positive definite functions on ordered groups.”

Hahn's Embedding Theorem for orders and harmonic analysis on groups with ordered duals

Nakhlé Asmar, Stephen Montgomery-Smith (1996)

Colloquium Mathematicae

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Let G be a locally compact abelian group whose dual group Γ contains a Haar measurable order P. Using the order P we define the conjugate function operator on L p ( G ) , 1 ≤ p < ∞, as was done by Helson [7]. We will show how to use Hahn’s Embedding Theorem for orders and the ergodic Hilbert transform to study the conjugate function. Our approach enables us to define a filtration of the Borel σ-algebra on G, which in turn will allow us to introduce tools from martingale theory into the analysis...

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...

On generalized d'Alembert functional equation.

Mohamed Akkouchi, Allal Bakali, Belaid Bouikhalene, El Houcien El Qorachi (2006)

Extracta Mathematicae

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Let G be a locally compact group. Let σ be a continuous involution of G and let μ be a complex bounded measure. In this paper we study the generalized d'Alembert functional equation D(μ)    ∫G f(xty)dμ(t) + ∫G f(xtσ(y))dμ(t) = 2f(x)f(y) x, y ∈ G; where f: G → C to be determined is a measurable and essentially bounded function.