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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.… Expand

Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions

- C. Berg, J. Christensen, P. Ressel
- Mathematics
- 1984

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… Expand

Integral Representation of Some Functions Related to the Gamma Function

- C. Berg
- Mathematics
- 24 November 2004

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.

Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity

- C. Berg
- Mathematics
- 2007

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… Expand

Exponentially bounded positive definite functions

- C. Berg, P. H. Maserick
- Mathematics
- 1 March 1984

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… Expand

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.… Expand

A remark on the multidimensional moment problem

- C. Berg, J. Christensen, C. U. Jensen
- Mathematics
- 1 June 1979

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… Expand

The Cube of a Normal Distribution is Indeterminate

- C. Berg
- Mathematics
- 1 April 1988

On montre que si X est une variable aleatoire de distribution normale, alors X 2n+1 a une distribution indeterminee pour n≥1

On Powers of Stieltjes Moment Sequences, I

- C. Berg
- Mathematics
- 1 October 2005

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… Expand

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