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General Stieltjes moment problems for rapidly decreasing smooth functions

(2017) STUDIA MATHEMATICA. 238(3). p.271-295
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Abstract
We give ( necessary and sufficient) conditions on a sequence {f(n)}n(infinity)=0 of functions under which every generalized Stieltjes moment problem integral(infinity)(0) f(n) (x) phi (x) dx = a(n), n epsilon N, has solutions phi epsilon S(R) with supp phi subset of [0, infinity). Furthermore, we consider more general problems of this kind for measure or distribution sequences {f(n)} n(infinity)=0. We also study vector moment problems with values in Frechet spaces and multidimensional moment problems.
Keywords
Stieltjes moment problems, rapidly decreasing smooth solutions, GELFAND-SHILOV SPACES, FOURIER-TRANSFORMS, RADIAL FUNCTIONS, DISTRIBUTIONS, OPERATORS

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Chicago
Estrada, Ricardo, and Jasson Vindas Diaz. 2017. “General Stieltjes Moment Problems for Rapidly Decreasing Smooth Functions.” Studia Mathematica 238 (3): 271–295.
APA
Estrada, R., & Vindas Diaz, J. (2017). General Stieltjes moment problems for rapidly decreasing smooth functions. STUDIA MATHEMATICA, 238(3), 271–295.
Vancouver
1.
Estrada R, Vindas Diaz J. General Stieltjes moment problems for rapidly decreasing smooth functions. STUDIA MATHEMATICA. 2017;238(3):271–95.
MLA
Estrada, Ricardo, and Jasson Vindas Diaz. “General Stieltjes Moment Problems for Rapidly Decreasing Smooth Functions.” STUDIA MATHEMATICA 238.3 (2017): 271–295. Print.
@article{8520735,
  abstract     = {We give ( necessary and sufficient) conditions on a sequence \{f(n)\}n(infinity)=0 of functions under which every generalized Stieltjes moment problem 

integral(infinity)(0) f(n) (x) phi (x) dx = a(n), n epsilon N, 

has solutions phi epsilon S(R) with supp phi subset of [0, infinity). Furthermore, we consider more general problems of this kind for measure or distribution sequences \{f(n)\} n(infinity)=0. We also study vector moment problems with values in Frechet spaces and multidimensional moment problems.},
  author       = {Estrada, Ricardo and Vindas Diaz, Jasson},
  issn         = {0039-3223},
  journal      = {STUDIA MATHEMATICA},
  keyword      = {Stieltjes moment problems,rapidly decreasing smooth solutions,GELFAND-SHILOV SPACES,FOURIER-TRANSFORMS,RADIAL FUNCTIONS,DISTRIBUTIONS,OPERATORS},
  language     = {eng},
  number       = {3},
  pages        = {271--295},
  title        = {General Stieltjes moment problems for rapidly decreasing smooth functions},
  url          = {http://dx.doi.org/10.4064/sm8728-3-2017},
  volume       = {238},
  year         = {2017},
}

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