M. Alfaro

activity

19962013

most citedOrthogonal polynomials generated by a linear structure relation: Inverse problem

13 citations · 22 across the 7 of their papers we have counts for

collaborators

7 papers

math.CA2013★ 6 cited

On linearly related orthogonal polynomials in several variables

M. Alfaro, A. Peña, T. E. Pérez +1

Let ${P_{n}}_{n \geq 0}$ and ${Q_{n}}_{n \geq 0}$ be two monic polynomial systems in several variables satisfying the linear structure relation $$\mathbb{Q}_n = \math…

math.CA2012★ 13 cited

Orthogonal polynomials generated by a linear structure relation: Inverse problem

M. Alfaro, A. Peña, J. Petronilho +1

Let $(P_{n})_{n}$ and $(Q_{n})_{n}$ be two sequences of monic polynomials linked by a type structure relation such as $Q_{n} (x) + r_{n} Q_{n - 1} (x) = P_{n} (x) + s_{n} P_{n - 1} (x) + t_{n} P_{n - 2} (x),$ w…

math.CA2009★ 1 cited

Orthogonal polynomials associated with an inverse quadratic spectral transform

M. Alfaro, F. Marcellan, A. Pena +1

Let ${P_{n}}_{n \geq 0}$ be a sequence of monic orthogonal polynomials with respect to a quasi--definite linear functional $u$ and ${Q_{n}}_{n \geq 0}$ a sequence of polynomials define…

math.CA2009

Asymptotics for a generalization of Hermite polynomials

M. Alfaro, J. J. Moreno-Balcazar, A. Pena +1

We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied…

math.CA2007★ 2 cited

When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?

M. Alfaro, F. Marcellan, A. Pena +1

Given ${P_{n}}$ a sequence of monic orthogonal polynomials, we analyze their linear combinations ${Q_{n}}$ with constant coefficients and fixed length $k + 1$ . Necessary and suffici…

math.CA2006

Sobolev orthogonal polynomials: balance and asymptotics

M. Alfaro, J. J. Moreno-Balcazar, A. Pena +1

Let $μ_{0}$ and $μ_{1}$ be measures supported on an unbounded interval and $S_{n, λ_{n}}$ the extremal varying Sobolev polynomial which minimizes \begin{equation*} < P, P >_{λ_n}=\int P^2…