Generalized polynomials and associated semigroups

Name: Generalized polynomials and associated semigroups
Brand: Balderrama, Cristina
SKU: NW-9786131523786
Price: 39.0 EUR
Availability: InStock

Le Pitch

PrésentationIn 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. Afficher moinsAfficher plus

Balderrama, Cristina

Generalized polynomials and associated semigroups

39,00 €

Le Pitch

PrésentationIn 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. Afficher moinsAfficher plus