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 M. Necessary and sufficient conditions on 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-2-2,
author = {Alberto Lastra and Javier Sanz},
title = {Stieltjes moment problem in general Gelfand-Shilov spaces},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {111-128},
zbl = {1188.47015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-2-2}
}
Alberto Lastra; Javier Sanz. Stieltjes moment problem in general Gelfand-Shilov spaces. Studia Mathematica, Tome 192 (2009) pp. 111-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-2-2/