Generalized polynomials and associated semigroups

Generalized orthogonal polynomials with hermitian matrix argument and associated semigroups

Cristina Balderrama - Collection Omn.univ.europ.

120 pages, parution le 31/10/2010

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Résumé

In this work we construct and study families of generalized orthogonal polynomials with hermitian matrix argument associated to a family of orthogonal polynomials on R. Different normalizations for these polynomials are considered and we obtain some classical formulas for orthogonal polynomials from the corresponding formulas for the one-dimensional polynomials. We also construct semigroups of operators associated to the generalized orthogonal polynomials and we give an expression of the infinitesimal generator of this semigroup and, in the classical cases, we prove that this semigroup is also Markov. For d-dimensional Jacobi expansions we study the notions of fractional integral (Riesz potentials), Bessel potentials and fractional derivatives. We present a novel decomposition of the L2 space associated with the d-dimensional Jacobi measure and obtain an analogous of Meyer's multiplier theorem in this setting. Sobolev Jacobi spaces are also studied.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Editions universitaires européennes
Auteur(s)	Cristina Balderrama
Collection	Omn.univ.europ.
Parution	31/10/2010
Nb. de pages	120
Format	15 x 22
Couverture	Broché
Poids	188g
EAN13	9786131523786