Modifications of quasi-definite linear functionals via addition of delta and derivatives of delta Dirac functions

20 pages, no figures.-- MSC2000 codes: 33C45, 33A65, 42C05.MR#: MR2061464 (2005b:33007)Zbl#: Zbl 1089.33005We consider the general theory of the modifications of quasi-definite linear functionals by adding discrete measures. We analyze the existence of the corresponding orthogonal polynomial sequences with respect to such linear functionals. The three-term recurrence relation, lowering and raising operators as well as the second order linear differential equation that the sequences of monic orthogonal polynomials satisfy when the linear functional is semiclassical are also established. A relevant example is considered in details.This work is partially supported by Dirección General de Investigacion (Ministerio de Ciencia y Tecnología) of Spain BFM 2000-0206-C04, Junta de Andalucía FQM-0262, and INTAS n° 2000-272.Publicad