The Sobolev-type moment problem

9 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.This research carried out within the framework of scientific and technical cooperation between Spain and Poland was supported by the Ministry of Foreign Affairs of Spain and the Committee of Scientific Research (KBN) of Poland, grand 07/R98. The work of Francisco Marcellán was also partially supported by Dirección General de Enseñanza Superior (DGES) of Spain, grant PB96-0120C03-01 and INTAS project INTAS-93-219Ext.Publicad