Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 26 Sep 2020 03:15:17 GMT2020-09-26T03:15:17Z5051On some tridiagonal k-Toeplitz matrices: Algebraic and analytical aspects. Applicationshttp://hdl.handle.net/10316/4620Title: On some tridiagonal k-Toeplitz matrices: Algebraic and analytical aspects. Applications
Authors: Álvarez-Nodarse, R.; Petronilho, J.; Quintero, N. R.
Abstract: 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.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/46202005-01-01T00:00:00ZOn the Krall-type discrete polynomialshttp://hdl.handle.net/10316/4636Title: On the Krall-type discrete polynomials
Authors: Álvarez-Nodarse, R.; Petronilho, J.
Abstract: 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.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/46362004-01-01T00:00:00ZWKB Approximation and Krall-Type Orthogonal Polynomialshttp://hdl.handle.net/10316/7743Title: WKB Approximation and Krall-Type Orthogonal Polynomials
Authors: Álvarez-Nodarse, R.; Marcellán, F.; Petronilho, J.
Abstract: 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 explicitly, aswell as some asymptotic formulas. With special emphasis will be consideredthe second order differential equations that such polynomials satisfy. Theyallow us to obtain the central moments and the WKB approximation of thedistribution of zeros. Some examples coming from quadratic polynomialmappings and tridiagonal periodic matrices are also studied.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10316/77431998-01-01T00:00:00ZOn properties of hypergeometric type-functionshttp://hdl.handle.net/10316/11334Title: On properties of hypergeometric type-functions
Authors: Cardoso, J. L.; Fernandes, C.; Alvarez-Nodarse, R.
Abstract: 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 the condition […] 0, where _ is an arbitrary complex (fixed) number. We also assume
that the coefficients of the polynomials _ and _ do not depend on _. To this class
of functions belong Gauss, Kummer and Hermite functions, and also the classical
orthogonal polynomials. In this work, using the constructive approach introduced
by Nikiforov and Uvarov, several structural properties of the hypergeometric type
functions y = y_(z) are obtained. Applications to hypergeometric functions and
classical orthogonal polynomials are also given
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/113342006-01-01T00:00:00ZPointwise convergent expansions in q-Fourier-Bessel serieshttp://hdl.handle.net/10316/11343Title: Pointwise convergent expansions in q-Fourier-Bessel series
Authors: Abreu, L. D.; Alvarez-Nodarse, R.; Cardoso, J. L.
Abstract: We define q-analogues of Fourier-Bessel series, by means of complete q-
orthogonal systems constructed with the third Jackson q-Bessel function. Sufficient
conditions for pointwise convergence of these series are obtained, in terms of a
general convergence principle valid for other Fourier series on grids defined over
numerable sets. The results are illustrated with specific examples of developments
in q-Fourier-Bessel series.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/113432006-01-01T00:00:00Z