Encontrados 8 documentos, a visualizar página 1 de 1
On linearly related sequences of derivatives of orthogonal polynomials
Jesus, M. N. de; Petronilho, J.We discuss an inverse problem in the theory of (standard) orthogonal polynomials involving two orthogonal polynomial families (Pn)n and (Qn)n whose derivatives of higher orders m and k (resp.) are connected by a linear algebraic structure relation such as for all n=0,1,2,..., where M and N are fixed nonnegative integer numbers, and ri,n and si,n are given complex parameters satisfying some natural conditions. L...
Orthogonal polynomials on the unit circle via a polynomial mapping on the real ...
Petronilho, J.Let [Phi]nn[greater-or-equal, slanted]0 be a sequence of monic orthogonal polynomials on the unit circle (OPUC) with respect to a symmetric and finite positive Borel measure d[mu] on [0,2[pi]] and let -1,[alpha]0,[alpha]1,[alpha]2,... be the associated sequence of Verblunsky coefficients. In this paper we study the sequence of monic OPUC whose sequence of Verblunsky coefficients iswhere b1,b2,...,bN-1 are N-1 f...
On the linear functionals associated to linearly related sequences of orthogona...
Petronilho, J.An inverse problem is solved, by stating that the regular linear functionals u and v associated to linearly related sequences of monic orthogonal polynomials (Pn)n and (Qn)n, respectively, in the sense for all n=0,1,2,... (where ri,n and si,n are complex numbers satisfying some natural conditions), are connected by a rational modification, i.e., there exist polynomials [phi] and [psi], with degrees M and N, res...
On some tridiagonal k-Toeplitz matrices: Algebraic and analytical aspects. Appl...
Álvarez-Nodarse, R.; Petronilho, J.; Quintero, N. R.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 model. Some numerical experiments are also included. ; http://www.sciencedirect.com/science/article/B6TYH-4FSCV...
Explicit inverse of a tridiagonal k-Toeplitz matrix
Fonseca, C. M. da; Petronilho, J.Summary We obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal k-Toeplitz matrix A. The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of Chebyshev polynomials of the second kind. We also compute the characteristic polynomial of A which enables us to state som...
On the Krall-type discrete polynomials
Álvarez-Nodarse, R.; Petronilho, J.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 satisfy are established. Some relevant examples of q-Krall polynomials are considered in detail. ; http://www....
Explicit inverses of some tridiagonal matrices
Fonseca, C. M. da; Petronilho, J.We give explicit inverses of tridiagonal 2-Toeplitz and 3-Toeplitz matrices which generalize some well-known results concerning the inverse of a tridiagonal Toeplitz matrix. ; http://www.sciencedirect.com/science/article/B6V0R-42KDHCJ-2/1/d6207c3bf9c66184210a9296f72fe1e5
WKB Approximation and Krall-Type Orthogonal Polynomials
Álvarez-Nodarse, R.; Marcellán, F.; Petronilho, J.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 some properties of the Krall-type polynomials arestudied. The three-term recurrence relation is calculated explici...
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