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author = "Alvarez-Nodarse, R."
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Found 16 documents, displaying page 1 of 2

On the Krall-type discrete polynomials

Author(s) : Álvarez-Nodarse, R. , Petronilho, J.
Description : In this paper we present a unified theory for studying the so-called Krall-type discrete orthogonal polynomials. In particular, the three-term recurrence relation, lowering and raising operators as well as the second order linear difference equation that the sequences of monic orthogonal polynomials...
Repository : Estudo Geral
Language(s) : English

On properties of hypergeometric type-functions

Author(s) : Cardoso, J. L. , Fernandes, C. , Alvarez-Nodarse, R.
Description : The functions of hypergeometric type are the solutions y = y_(z) of the differential equation _(z)y′′+_ (z)y′+_y = 0, where _ and _ are polynomials of degrees not higher than 2 and 1, respectively, and _ is a constant. Here we consider a class of functions of hypergeometric type: those that satisfy ...
Repository : Estudo Geral
Language(s) : English

On some tridiagonal k-Toeplitz matrices: Algebraic and analytical aspects. Applications

Author(s) : Álvarez-Nodarse, R. , Petronilho, J. , Quintero, N. R.
Description : In this paper, we use the analytic theory for 2 and 3-Toeplitz matrices to obtain the explicit expressions for the eigenvalues, eigenvectors and the spectral measure associated to the corresponding infinite matrices. As an application we consider two solvable models related with the so-called chain ...
Repository : Estudo Geral
Language(s) : English

WKB Approximation and Krall-Type Orthogonal Polynomials

Author(s) : Álvarez-Nodarse, R. , Marcellán, F. , Petronilho, J.
Description : We give a unified approach to the Krall-type polynomials orthogonal withrespect to a positive measure consisting of an absolutely continuous one‘perturbed’ by the addition of one or more Dirac deltafunctions. Some examples studied by different authors are considered from aunique point of view. Also ...
Repository : Estudo Geral
Language(s) : English

Factorization method for difference equations of hypergeometric type on nonuniform lattices

Author(s) : Álvarez-Nodarse, R. , Costas-Santos, R. S.
Description : We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given. , Comment: 21 pages
Repository : arXiv
Language(s) : Undetermined

The orthogonality of q-classical polynomials of the Hahn class: A geometrical approach

Author(s) : Alvarez-Nodarse, R. , Sevinik-Adiguzel, R. , Taseli, H.
Description : The idea of this review article is to discuss in a unified way the orthogonality of all positive definite polynomial solutions of the $q$-hypergeometric difference equation on the $q$-linear lattice by means of a qualitative analysis of the $q$-Pearson equation. Therefore, our method differs from ...
Repository : arXiv
Language(s) : Undetermined

On the orthogonality of q-classical polynomials of the Hahn class II

Author(s) : Alvarez-Nodarse, R. , Sevinik-Adiguzel, R. , Taseli, H.
Description : In this article, the study of the orthogonality properties of $q$-polynomials of the Hahn class started in the initial article by R. \'Alvarez-Nodarse, R. Sevinik-Ad{\i}g\"uzel, and H. Ta\c{s}eli, \textit{On the orthogonality of $q$-classical polynomials of the Hahn class I} is proceeded. To be mo...
Repository : arXiv
Language(s) : Undetermined

The q-Racah-Krall-type polynomials

Author(s) : Alvarez-Nodarse, R. , Sevinik-Adiguzel, R.
Description : In this paper the Krall-type polynomials obtained via the addition of two mass points to the weight function of the \textit{standard} $q$-Racah polynomials are introduced. Several algebraic properties of these polynomials are obtained and some of their limit cases are discussed.
Repository : arXiv
Language(s) : Undetermined

On the Properties of Special Functions on the linear-type lattices

Author(s) : Alvarez-Nodarse, R. , Cardoso, J. L.
Description : We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particula...
Repository : arXiv
Language(s) : Undetermined

Limit relations between $q$-Krall type orthogonal polynomials

Author(s) : Álvarez-Nodarse, R. , Costas-Santos, R. S.
Description : In this paper, we consider a natural extension of several results related to Krall-type polynomials introducing a modification of a $q$-classical linear functional via the addition of one or two mass points. The limit relations between the $q$-Krall type modification of big $q$-Jacobi, little $q$-...
Repository : arXiv
Language(s) : Undetermined
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Found 16 documents, displaying page 1 of 2