In this paper we study how an inner product derived from an Uvarov
transformation of the Laguerre weight function is used in the
orthogonalization procedure of a sequence of martingales related to a Levy
process. The orthogonalization is done by isometry. The resulting set of
pairwise strongly orthogonal martingales involved are used as integrators in
the so-called chaotic representation propertyEdmundo J. Huertas is supported by a grant from Ministerio de Ciencia e Innovación (MTM
2009-12740-C03-01), and by Fundação para a Ciência e Tecnologia (FCT), ref.
SFRH/BPD/91841/2012, Portugal. Nuria Torrado is supported by Fundação para a Ciência e Tecnologia (FCT), ref.
SFRH/BPD/91832/2012, Portugal. The research of Fabrizio Leisen has been partially supported by the Spanish
Ministry of Science and Innovation through grant ECO2011-2570
