Linear continuous operators for the Stieltjes moment problem in Gelfand-Shilov spaces

We obtain linear continuous operators providing a solution to the Stieltjes moment problem in the framework of Gelfand-Shilov spaces of rapidly decreasing smooth functions. The construction rests on an interpolation procedure due to R. Estrada for general rapidly decreasing smooth functions, and adapted by S.-Y Chung, D. Kim and Y. Yeom to the case of Gelfand-Shilov spaces. It requires a linear continuous version of the so-called Borel-Ritt-Gevrey theorem in asymptotic theory. (C) 2007 Elsevier Inc. All rights reserved.