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Harmonic Analysis on Semigroups
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Potential Theory on Locally Compact Abelian Groups
I. Harmonic Analysis.- 1. Notation and Preliminaries.- 2. Some Basic Results From Harmonic Analysis.- 3. Positive Definite Functions.- 4. Fourier Transformation of Positive Definite Measures.- 5.…
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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
1 Introduction to Locally Convex Topological Vector Spaces and Dual Pairs.- 1. Locally Convex Vector Spaces.- 2. Hahn-Banach Theorems.- 3. Dual Pairs.- Notes and Remarks.- 2 Radon Measures and…
Integral Representation of Some Functions Related to the Gamma Function
Abstract.We prove that the functions $$\Phi (x) = [\Gamma (x + 1)]^{1/x} (1 + 1/x)^x /x$$ and $$\log \Phi (x)$$ are Stieltjes transforms.
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Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity
This paper is mainly a survey of published results. We recall the definition of positive definite and (conditionally) negative definite functions on abelian semigroups with involution, and we…
Exponentially bounded positive definite functions
Equivalent conditions for scalar (or operator valued) positive definite functions, on a commutative semigroup $ with identity e, to admit a disintegration with respect to a regular positive (operator…
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Some classes of completely monotonic functions
We prove: (i) Let F n (r) = P n (x)[e - (1 + 1/x) x ] and G n (x) = P n (x)[(1 + 1/x) x + 1 - e], where P n (x) = x n + Σ n - 1 v = 0 c v , x v is a polynomial of degree n > 1 with real coefficients.…
A remark on the multidimensional moment problem
To mot ivate the following results let us recall some definitions and results with relation to the m o m e n t problem. Let (S, + ) be an abelian semigroup with neutral element 0. A real-valued…
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The Cube of a Normal Distribution is Indeterminate
On montre que si X est une variable aleatoire de distribution normale, alors X 2n+1 a une distribution indeterminee pour n≥1
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On Powers of Stieltjes Moment Sequences, I
For a Bernstein function f the sequence sn=f(1)·...· f(n) is a Stieltjes moment sequence with the property that all powers snc,c>0 are again Stieltjes moment sequences. We prove that $$s_n^c$$ is…
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