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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Sobolev-type moment problem


Authors: Francisco Marcellán and Franciszek Hugon Szafraniec
Journal: Proc. Amer. Math. Soc. 128 (2000), 2309-2317
MSC (2000): Primary 44A99; Secondary 47B15, 47B20, 47B25
DOI: https://doi.org/10.1090/S0002-9939-00-05535-0
Published electronically: February 25, 2000
MathSciNet review: 1694873
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Abstract: We 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.


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Additional Information

Francisco Marcellán
Affiliation: Departamento de Matemáticas, Universidad Carlos III de Madrid, c/Butarque, 15, E-28911 Leganés, Spain
Email: pacomarc@ing.uc3m.es

Franciszek Hugon Szafraniec
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, PL-30059 Kraków, Poland
Email: fhszafra@im.uj.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-00-05535-0
Received by editor(s): September 10, 1998
Published electronically: February 25, 2000
Additional Notes: 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.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society