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Stieltjes moment problem in general Gelfand–Shilov spaces

Tom 192 / 2009

Alberto Lastra, Javier Sanz Studia Mathematica 192 (2009), 111-128 MSC: Primary 47A57; Secondary 30E05, 44A60. DOI: 10.4064/sm192-2-2

Streszczenie

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.

Autorzy

  • Alberto LastraDepartamento de Análisis Matemático y Didáctica de
    la Matemática
    Facultad de Ciencias
    Universidad de Valladolid
    Paseo del Prado de la Magdalena s//n
    47005 Valladolid, Spain
  • Javier SanzDepartamento de Análisis Matemático y Didáctica de
    la Matemática
    Facultad de Ciencias
    Universidad de Valladolid
    Paseo del Prado de la Magdalena s//n
    47005 Valladolid, Spain
    e-mail

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