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On a polynomial sequence associated with the Bessel operator

Authors: Ana F. Loureiro, P. Maroni and S. Yakubovich
Journal: Proc. Amer. Math. Soc. 142 (2014), 467-482
MSC (2010): Primary 33C45, 42C05, 44A15, 44A20
Published electronically: October 18, 2013
MathSciNet review: 3133989
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Abstract | References | Similar Articles | Additional Information

Abstract: By means of the Bessel operator a polynomial sequence is constructed to which several properties are given. Among them are its explicit expression, the connection with the Euler numbers, and its integral representation via the Kontorovich-Lebedev transform. Despite its non-orthogonality (with respect to an $ L_{2}$-inner product), it is possible to associate to the canonical element of its dual sequence a positive-definite measure as long as certain stronger constraints are imposed.

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Additional Information

Ana F. Loureiro
Affiliation: CMUP and DM-FCUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
Address at time of publication: School of Mathematics, Statistics & Actuarial Science (SMSAS), Cornwallis Building, University of Kent, Canterbury, Kent, CT2 7NF, United Kingdom

P. Maroni
Affiliation: CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France

S. Yakubovich
Affiliation: CMUP and DM-FCUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal

Received by editor(s): April 20, 2011
Received by editor(s) in revised form: December 20, 2011
Published electronically: October 18, 2013
Additional Notes: The work of the first author was supported by Fundação para a Ciência e Tecnologia via the grant SFRH/BPD/63114/2009.
The research of the first and third authors was partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese government through the FCT (Fundação para a Ciência e a Tecnologia) under the project PEst-C/MAT/UI0144/2011.
Communicated by: Walter Van Assche
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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