The Stieltjes Moment Problem with Complex Exponents

Abstract. We give (necessary and sufficient) conditions over a sequence {f n } ∞ n=0of functions under which every generalized Stieltjes moment problemhas solutions φ ∈ S(R) with supp φ ⊆ [0, ∞). Furthermore, we consider more general problems of this kind for measure or distribution sequences {f n } ∞ n=0 . We also study vector moment problems with values in Fréchet spaces and multidimensional moment problems.

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“…. are completely discontinuous with respect 5 The map T is actually bicontinuous with respect to the topology of pointwise convergence in C N .…”

Section: Density Of the Set Of Solutions Of Moment Problemsmentioning

confidence: 99%

“…The corresponding generalization for the strong moment problem has been given in [6]. Extensions of these results to vector-valued Stieltjes moment problems are also well-known [5,7,14]. Chung, Chung, and Kim, and more recently, Lastra and Sanz have considered moment problems with solutions in Gelfand-Shilov classes [3,17,18].…”

Section: Introductionmentioning

confidence: 98%

General Stieltjes moment problems for rapidly decreasing smooth functions

Estrada

Vindas

2017

Studia Math.

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The Hausdorff Moment Problem with Complex Exponents and a Müntz‐Szasz Theorem for Distributions

Durán

1997

Mathematische Nachrichten

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This paper deals with a Hausdorff moment problem with complex exponents, that is, given a sequence of complex numbers (zn), and a fixed space X of functions defined on [O, 11, we ask under which conditions on a sequence ( u~)~ the moment problem a, = & l t " -f ( t ) dt for n E N has a solution in the space X. Mainly, we study the solution belonging to the space 'D[o,JI. The results which we will obtain will lead us to prove a Miinta-Szass Theorem for distributions.First, we study and solve when the Hausdorff moment problem always has a solution, that is, we characterize in a simple way the complex sequences (z,), satisfying that for every complex sequence (a,), there exists a function f such that the functions t z n f ( t ) are Lebesgue integrable in [0,1] and a, = 1 ; tznf(t) dt. In fact, a necessary and sufficient condition on (z,), is the following: If we put p = inf {%z, : n 2 0}, then limn %z, = p, %z, # p for all n 2 0, and z, # zm if n # m. This result completes

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The vector-valued Stieltjes moment problem with general exponents

Debrouwere,

Neyt

2024

Banach J. Math. Anal.

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The Stieltjes Moment Problem with Complex Exponents

Cited by 3 publications

References 10 publications

General Stieltjes moment problems for rapidly decreasing smooth functions

General Stieltjes moment problems for rapidly decreasing smooth functions

The Hausdorff Moment Problem with Complex Exponents and a Müntz‐Szasz Theorem for Distributions

The vector-valued Stieltjes moment problem with general exponents

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