✦ LIBER ✦
The Hausdorff Moment Problem with Complex Exponents and a Müntz-Szasz Theorem for Distributions
✍ Scribed by Antonio J. Duran
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 856 KB
- Volume
- 187
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
This paper deals with a Hausdorff moment problem with complex exponents, that is, given a sequence of complex numbers (z~n~)n and a fixed space X of functions denned on [0, 1], we ask under which conditions on a sequence (a~n~)~n~ the moment problem a~n~ = ∫ t^Zn^ 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.