Stieltjes moment problem in general Gelfand–Shilov spaces
Volume 192 / 2009
Studia Mathematica 192 (2009), 111-128
MSC: Primary 47A57; Secondary 30E05, 44A60.
DOI: 10.4064/sm192-2-2
Abstract
The Stieltjes moment problem is studied in the framework of general Gelfand–Shilov spaces, subspaces of the space of rapidly decreasing smooth complex functions, which are defined by imposing suitable bounds on their elements in terms of a given sequence $\boldsymbol M$. Necessary and sufficient conditions on $\boldsymbol M$ are stated for the problem to have a solution, sometimes coming with linear continuous right inverses of the moment map, sending a function to the sequence of its moments. On the way, some results on the existence of continuous right inverses for the Borel map are obtained for ultraholomorphic classes in sectors.
