K. Castillo

activity

20152026

most citedAn electrostatic interpretation of the zeros of sieved ultraspherical polynomials

5 citations · 7 across the 26 of their papers we have counts for

collaborators

29 papers

math.CA2026

The lower envelope of ultraspherical polynomials

K. Castillo, S. Sadigova

Let $R_{n}^{(a, b)} = P_{n}^{(a, b)} / P_{n}^{(a, b)} (1)$ be the normalised Jacobi polynomials. For $α \geq 0$ , put $ξ_{0} = - 1$ and let $ξ_{n}$ be the largest zero of $R_{n}^{(α + 1, α)}$ for $n \geq 1$ . We pr…

math.CA2026

Affine Scaling of Jacobi Zeros: Sharp Orderings Beyond Gautschi's Conjectures

K. Castillo, F. R. Rafaeli

We settle two conjectures of Gautschi on the degree dependence of the zeros of the Jacobi polynomials $P_{n}^{(α, β)}$ , $α, β > - 1$ , and obtain results substantially stronger than those…

math.CA2026

A proof of the Szegő conjecture on Jacobi extrema

K. Castillo

For Jacobi polynomials with parameters greater than $- 1/2$ , and with the relative extrema enumerated from the endpoint $x = 1$ , the normalised modulus at the $k$ th extremum of degree…

math.CA2026

Wendroff's theorem beyond consecutive degrees and related inverse spectral problems

K. Castillo, G. Gordillo-Núñez

A classical theorem of Wendroff shows that one may reconstructs a sequence of orthogonal polynomials on the real line from two non-constant polynomials of consecutive degrees whose…

math.SP2023★ 1 cited

Remark on the eigenvalues of a tridiagonal matrix in biogeography

K. Castillo

The main result proved in [The eigenvalues of a tridiagonal matrix in biogeography, Appl. Math. Comput. 218 (2011) 195-201; MR2821464] by B. Igelnik and D. Simon is virtually the S…

math.CA2023

Epilegomena to the study of semiclassical orthogonal polynomials

K. Castillo, D. Mbouna

In his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005 (paperback edition 2009)], Ismail conjectured that certain structur…