Raising and lowering operators, factorization and differential/difference operators of hypergeometric type
نویسنده
چکیده
Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type. PACS: 02.10Nj; 02.20.Sv; 02.70.Bf; 03.65.Ge
منابع مشابه
Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice
We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on nonhomogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely, those difference of orthogonal polynomials that satisfy a similar difference equation of hypergeometric type. PACS Numbers: 0210N, 0220S, 0230V, 027...
متن کاملCreation and Annihilation Operators for Orthogonal Polynomials of Continuous and Discrete Variables
We develop general expressions for the raising and lowering operators that belong to the orthogonal polynomials of hypergeometric type with discrete and continuous variable. We construct the creation and annihilation operators that correspond to the normalized polynomials and study their algebraic properties in the case of the Kravchuk/Hermite Meixner/Laguerre polynomials. 1. Introduction. In a...
متن کاملFactorization of self-adjoint ordinary differential equations
Keyword: Factorization method Self-adjoint differential equations Eigenvalue problems This paper deals with the factorization of self-adjoint differential operators Lð2nÞ 1⁄4 1 q d n dx qb d n dx , and their spectral type differential equations. Sufficient conditions of factorization are reported. A large class of differential operators and equations that can be factorized is obtained. The fact...
متن کاملFrom torsion theories to closure operators and factorization systems
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
متن کاملOn some properties of q-Hahn multiple orthogonal polynomials
This contribution deals with multiple orthogonal polynomials of type II with respect to q-discrete measures (q-Hahn measures). In addition, we show that this family of multiple orthogonal polynomials has a lowering operator, and raising operators as well as a Rodrigues type formula. The combination of lowering and raising operators leads to a third order q-difference equation when two orthogona...
متن کامل