Marcellán Español, Francisco JoséSzafraniec, Franciszek H.2009-12-172009-12-172000-08Proceedings of the American Mathematical Society, 2000, vol. 128, n. 8, p. 2309-23170002-9939 (Print)1088-6826 (Online)https://hdl.handle.net/10016/61439 pages, no figures.-- MSC2000 codes: Primary 44A99; Secondary 47B15, 47B20, 47B25.MR#: MR1694873 (2000k:44006)Zbl#: Zbl 0951.44002We propose necessary and sufficient conditions for a bisequence of complex numbers to be a moment one of Sobolev type over the real line, the unit circle and the complex plane. We achieve this through converting the moment problem in question into a matrix one and utilizing some techniques coming from operator theory. This allows us to consider the Sobolev type moment problem in its full generality, not necessarily in the diagonal case and even of infinite order.application/pdfeng© American Mathematical SocietySobolev-type moment problemPositive operatorsInner productOrthogonal polynomialsMoment sequence of Sobolev typeMatrix moment problemsresearch articleMatemáticasopen access