On the entropy for indeterminate moment problems
Abstract
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) entropy. These densities are either all bounded or all unbounded. The result is illustrated by the Al-Salam–Carlitz moment problem, where all the densities in the family are bounded.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Quantum Mechanics and Non-Hermitian Physics
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Electronic Communications in Probability
- Volume
- 31
- Issue
- none
- Publication date
- 1 January 2026