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math.CA2024
-potent Schwarz matrices and Bessel-like Jacobi polynomials
Alexander Dyachenko, Carlos M. da Fonseca, Mikhail Tyaglov
We consider the problem of the reconstruction of a Schwarz matrix from exactly one given eigenvalue. This inverse eigenvalue problem leads to the Jacobi orthogonal polynomials~$\{P…
math.CV2024
On the number of real zeroes of a homogeneous differential polynomial and a generalization of the Hawaii conjecture
Olga Katkova, Mikhail Tyaglov, Anna Vishnyakova
For a given real polynomial we study the possible number of real roots of a differential polynomial $H_{\varkappa}[p](x) = \varkappa\left(p'(x)\right)^2-p(x)p''(x), \varkappa \…