Premium
The Stieltjes Moment Problem with Complex Exponents
Author(s) -
Duran Antonio J.
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921580112
Subject(s) - mathematics , riemann–stieltjes integral , sequence (biology) , lebesgue integration , banach space , locally integrable function , moment (physics) , function (biology) , space (punctuation) , integrable system , combinatorics , moment problem , pure mathematics , discrete mathematics , mathematical analysis , physics , linguistics , philosophy , genetics , statistics , classical mechanics , evolutionary biology , principle of maximum entropy , biology , integral equation
In this paper, we characterize the complex sequences ( z n ) n which satisfy the following condition: For each complex sequence ( a n ) n , there exists a function f such that the functions t z n f ( t ) are Lebesgue integrable and a n = ∫ t z n f ( t )( dt ) for all n ∫. In this case, we give for every sequence ( a n ) n infinitely many C ∫ functions f satisfying some growth conditions in x = 0 and x = + ∫, and such that a n = ∫ t z n f ( t ) dt . Finally, we extend this result for Banach space valued functions.