RT Journal Article
T1 Orthogonal polynomials and quadratic transformations
A1 Marcellán Español, Francisco José
A1 Petronilho, José
AB Starting from a sequence $\{P_n\}_{n\geq 0}$ of monic polynomials orthogonal with respect to a linear functional ${\bf u}$, we find a linear functional ${\bf v}$ such that $\{Q_n\}_{\geq 0}$, with either $Q_{2n}(x)=P_n(T(x))$ or $Q_{2n+1}(x)=(x-a)\,P_n(T(x))$ where $T$ is a monic quadratic polynomial and $a\in\C$, is a sequence of monic orthogonal polynomials with respect to ${\bf v}$. In particular, we discuss the case when ${\bf u}$ and ${\bf v}$ are both positive definite linear functionals. Thus, we obtain a solution for an inverse problem which is a converse, for quadratic mappings, of one analyzed in [11].
PB European Mathematical Society
SN 0032-5155
YR 1999
FD 1999
LK https://hdl.handle.net/10016/6263
UL https://hdl.handle.net/10016/6263
LA eng
NO 33 pages, no figures.-- MSC1991 code: Primary 42C05.
NO MR#: MR1680116 (2000b:42021)
NO Zbl#: Zbl 0936.42012
NO This paper was finished with financial support of a Grant from Junta Nacional de Investigação Científica e Tecnológica (JNITC) - BD976 - and Centro de Matemática da Universidade de Coimbra (CMUC) of Portugal. The work of the first author was supported by the Dirección General de Enseñanza Superior (DGES) of Spain - PB96-0120-C03-01.
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RD 3 may. 2024