Christian Berg

activity

20242026

collaborators

5 papers

math.FA2026

Special N-extremal solutions to indeterminate moment problems

Christian Berg, Ryszard Szwarc

For an N-extremal solution $I^¼$ to an indeterminate moment problem it is known by a theorem of M. Riesz that the measure $(1 + x^{2})^{- 1} d I^¼ (x)$ is determinate. For $0 < I^\pm < 1$ we show b…

math.PR2025

On the entropy for indeterminate moment problems

Christian Berg

For an indeterminate Hamburger moment problem we consider an infinite family of analytic densities solving the moment problem and we prove that they all have finite (Shannon) entro…

math.CA2025

Analytic Versus Algebraic Density of Polynomials

Christian Berg, Brian Simanek, Richard Wellman

We show that under very mild conditions on a measure $I^¼$ on the interval $[0, \infty)$ , the span of ${x^{k}}_{k = n}^{\infty}$ is dense in $L^{2} (I^¼)$ for any $n = 0, 1, \dots$ . We presen…

math.CA2025

A complete Bernstein function related to the fractal dimension of Pascal's pyramid modulo a prime

Christian Berg

Let $f_{r} (x) = lo g (1 + r x) / lo g (1 + x)$ for $x > 0$ . We prove that $f_{r}$ is a complete Bernstein function for $0 \leq r \leq 1$ and a Stieltjes function for $1 \leq r$ . This answers a conjecture…

math.FA2024

Indeterminate Stieltjes moment problems revisited

Christian Berg

We consider a normalized indeterminate Hamburger moment sequence s which is supposed to be Stieltjes. We revisit old results about determinacy/indeterminacy in the sense of Stieltj…