arXiv subjects

C. Calderón

Publications and source records attributed to C. Calderón.

3 recordsLinked to original sources

arXiv2021

Structural formulas for matrix-valued orthogonal polynomials related to $2\times 2$ hypergeometric operators

We give some structural formulas for the family of matrix-valued orthogonal polynomials of size $2\times 2$ introduced by C. Calderón et al. in an earlier work, which are common eigenfunctions of a differential operator of hypergeometric type. Specifically, we give a Rodrigues formula that allows us to write this family of polynomials explicitly in terms of the classical Jacobi polynomials, and write, for the sequence of orthonormal polynomials, the three-term recurrence relation and the Christoffel-Darboux identity. We obtain a Pearson equation, which enables us to prove that the sequence of derivatives of the orthogonal polynomials is also orthogonal, and to compute a Rodrigues formula for these polynomials as well as a matrix-valued differential operator having these polynomials as eigenfunctions. We also describe the second-order differential operators of the algebra associated with the weight matrix.

math.CA↗

arXiv2018

$2\times2$ Hypergeometric operators with diagonal eigenvalues

In this work we classify all the order-two Hypergeometric operators $D$, symmetric with respect to some $2\times 2$ irreducible matrix-weight $W$ such that $DP_n=P_n\left(\begin{smallmatrix} λ_n&0\\0&μ_n \end{smallmatrix} \right)$ with no repetition among the eigenvalues $\{λ_n,μ_n\}_{n\in\mathbb N_0}$, where $\{P_n\}_{n\in\mathbb N_0}$ is the (unique) sequence of monic orthogonal polynomials with respect to $W$. We obtain, in a very explicit way, a three parameter family of such operators and weights. We also give the corresponding monic orthongonal polynomials, their three term recurrence relation and their squared matrix-norms.

math.CA↗

arXiv2012

Detecting lateral genetic material transfer

The bioinformatical methods to detect lateral gene transfer events are mainly based on functional coding DNA characteristics. In this paper, we propose the use of DNA traits not depending on protein coding requirements. We introduce several semilocal variables that depend on DNA primary sequence and that reflect thermodynamic as well as physico-chemical magnitudes that are able to tell apart the genome of different organisms. After combining these variables in a neural classificator, we obtain results whose power of resolution go as far as to detect the exchange of genomic material between bacteria that are phylogenetically close.

cs.NE↗