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

This paper deals with a Hausdorff moment problem with complex exponents, that is, given a sequence of complex numbers (zn)n and a fixed space X of functions denned on [0, 1], we ask under which conditions on a sequence (an)n the moment problem an = ∫  01 tZn f(t) dt for n ∈ IN has a solution in the space X. Mainly, we study the solution belonging to the space D[0, 1] The results which we will obtain will lead us to prove a Müntz‐Szasz Theorem for distributions.