The moment problem for a Sobolev inner product

17 pages, no figures.-- MSC2000 code: 44A60.MR#: MR1715024 (2000m:44013)Zbl#: Zbl 0980.44008The concepts of definite and determinate Sobolev moment problem are introduced. The study of these questions is reduced to the definiteness or determinacy, respectively, of a system of classical moment problems by means of a canonical decomposition of the moment matrix associated with a Sobolev inner product in terms of Hankel matrices.Research by second author (G.L.L.) was partially supported by Dirección General de Enseñanza Superior under Grant PB 96-0120-C03-01 and by INTAS under Grant 93-0219 EXT. Research by the third author (H.P.) was carried out while following a Doctoral Program at Universidad Carlos III de Madrid under a grant from Agencia Española de Cooperación Internacional.Publicad