On the attractor zero of a sequence of polynomials

Characterization of certain sequences of $q$-polynomials

A characterization is given of those sequences of quasi-orthogonal polynomials which form also $q$-Appell sets.

Averages along polynomial sequences in discrete nilpotent groups: singular Radon transforms

We consider a class of operators defined by taking averages along polynomial sequences in discrete nilpotent groups. In this paper we prove $L^2$ boundedness of discrete singular Radon transforms along general polynomial sequences in discrete nilpotent groups of step 2.

On a 2-orthogonal polynomial sequence via quadratic decomposition

We apply a symbolic approach of the general quadratic decomposition of polynomial sequences - presented in a previous article referenced herein - to polynomial sequences fulfilling specific orthogonal conditions towards two given functionals $u_{0},u_{1}$ belonging to the dual of the vector space of polynomials with coefficients in $\mathbb{C}$. The general quadratic decomposition produces four new sets of polynomials whose properties are investigated with the help of the mentioned symbolic approach together with further commands which inquire relevant features, as for instance, the classical …

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

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 sufficient conditions are given for the orthogonality of the monic sequence $\{Q_n \}$ as well as an interesting interpretation in terms of the Jacobi matrices associated with $\{P_n \}$ and $\{Q_n \}$. Moreover, in the case $k=2$, we characterize the families $\{P_n \}$ such that the corresponding polynomials $\{Q_n \}$ are also orthogonal.

两个类切比雪夫多项式序列的性质

Properties of two Chebyshev-like polynomial sequences

研究通过修改第二类切比雪夫多项式生成函数得到两个多项式序列，获得其判别式和结式恒等式及部分不可约性结果，还指出与两类切比雪夫多项式的关联。

Differential equation and recurrence relations of the Sheffer-Appell polynomial sequence: A matrix approach

Motivated by the effective impact of the Pascal functional and the Wronskian matrices, we investigate several identities and differential equation for the Sheffer-Appell polynomial sequence by using matrix algebra. The matrix approach, which we have used in this article, is convenient to derive the generating functions of the Sheffer-Appell polynomial sequence. By means of examples, we apply and also illustrate our results to an extended class of polynomial sequences.