45 Result(s)

Article

Stability of Third Degree Linear Functionals and Rational Spectral Transformations

In this paper, we consider linear forms of the third degree class. This means that the Stieltjes function associated with the corresponding moment sequence satisfies a cubic equation with polynomial coefficien...

Imed Ben Salah, Francisco Marcellán… in Mediterranean Journal of Mathematics (2022)

Article

Discrete–Continuous Jacobi–Sobolev Spaces and Fourier Series

Let \(p\ge 1, \ell \in \mathbb {N}, \alpha ,\beta >-1\) p ≥ ...

Abel Díaz-González, Francisco Marcellán… in Bulletin of the Malaysian Mathematical Sci… (2021)

Article

Analytical Properties of Touchard-Based Hybrid Polynomials via Operational Techniques

In this paper, the Touchard-based Laguerre–Gould–Hopper polynomials are introduced by using operational techniques. We investigate many properties of such polynomials. In particular, generating functions, seri...

Francisco Marcellán, Saima Jabee… in Bulletin of the Malaysian Mathematical Sci… (2021)

Chapter and Conference Paper

Darboux Transformations for Orthogonal Polynomials on the Real Line and on the Unit Circle

Jacobi matrices constitute a communicating vessel between orthogonal polynomials on the real line (OPRL) and the theory of self-adjoint operators. In this context, commutation methods in operator theory lead t...

María José Cantero, Francisco Marcellán… in Orthogonal Polynomials: Current Trends and… (2021)

Chapter and Conference Paper

Discrete Semiclassical Orthogonal Polynomials of Class 2

In this contribution, discrete semiclassical orthogonal polynomials of class s ≤ 2 are studied. By considering all possible solutions of the Pearson equation, we obtain the canonical families in each class. We al...

Diego Dominici, Francisco Marcellán in Orthogonal Polynomials: Current Trends and… (2021)

Chapter and Conference Paper

From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals

In this contribution, we present an overview of standard orthogonal polynomials by using an algebraic approach. Discrete Darboux transformations of Jacobi matrices are studied. Next, we emphasize the role of s...

Juan C. García-Ardila, Francisco Marcellán, Misael E. Marriaga in Orthogonal Polynomials (2020)

Article

Christoffel Transformation for a Matrix of Bi-variate Measures

We consider the sequences of matrix bi-orthogonal polynomials with respect to the bilinear forms $$\left\langle {\cdot ,\cdot }\right\...

Juan C. García-Ardila, Manuel Mañas… in Complex Analysis and Operator Theory (2019)

Article

Linear Combinations of d-Orthogonal Polynomials

The regularity of a linear combination of r consecutive elements of a monic d-orthogonal polynomial sequence has been studied when $$(...

Francisco Marcellán, Abdessadek Saib in Bulletin of the Malaysian Mathematical Sci… (2019)

Article

Some New Identities Involving Sheffer–Appell Polynomial Sequences via Matrix Approach

In this contribution, some new identities involving Sheffer–Appell polynomial sequences using generalized Pascal functional and Wronskian matrices are deduced. As a direct application of them, identities invol...

Francisco Marcellán, Mohd Shadab, Saima Jabee in Mediterranean Journal of Mathematics (2019)

Article

On Freud–Sobolev type orthogonal polynomials

In this contribution we deal with sequences of monic polynomials orthogonal with respect to the Freud Sobolev-type inner product $$\be...

Luis E. Garza, Edmundo J. Huertas, Francisco Marcellán in Afrika Matematika (2019)

Article

Matrix Pearson Equations Satisfied by Koornwinder Weights in Two Variables

We consider Koornwinder’s method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koo...

Francisco Marcellán, Misael Marriaga, Teresa E. Pérez… in Acta Applicandae Mathematicae (2018)

Chapter

Finite Orthogonal Laurent Polynomials

In this work, orthogonal Laurent polynomials on the real line associated with a finite family of classical orthogonal polynomials (the so called Romanovski–Hermite polynomial sequence) are discussed. Their exp...

Francisco Marcellán, Anbhu Swaminathan in The Mathematics of the Uncertain (2018)

Chapter

On Co-polynomials on the Real Line and the Unit Circle

In this paper, we present an overview about algebraic and analytic aspects of orthogonal polynomials on the real line when finite modifications of the coefficients of the three-term recurrence relation they sa...

Kenier Castillo, Francisco Marcellán… in Operations Research, Engineering, and Cybe… (2017)

Article

An Extension of the Geronimus Transformation for Orthogonal Matrix Polynomials on the Real Line

We consider matrix polynomials orthogonal with respect to a sesquilinear form \({\langle{\cdot,\cdot}\rangle_W}\) ...

Juan Carlos García-Ardila, Luis E. Garza… in Mediterranean Journal of Mathematics (2016)

Article

Relative Asymptotics of Matrix Orthogonal Polynomials for Uvarov Perturbations: The Degenerate Case

Let \({\alpha}\) α ...

Hossain O. Yakhlef, Francisco Marcellán in Mediterranean Journal of Mathematics (2016)

Reference Work Entry In depth

Orthogonal Polynomials: Computation

Francisco Marcellán in Encyclopedia of Applied and Computational Mathematics (2015)