57 citations · 275 across the 73 of their papers we have counts for
7 papers · 1 filter
Finite-term recurrences in a generalized Bochner--Krall family
L. M. Anguas, D. Barrios Rolanía, B. Shapiro +1
We classify the differential operators \(T=z^j\partial_z^j+z^m\partial_z^\ell\), where \(0\le m<\ell\) and \(1\le j<\ell\), whose monic eigenpolynomials satisfy a finite-term recur…
In search of higher Bochner theorem
Emil Horozov, Boris Shapiro, Milos Tater
We initiate the study of a natural generalisation of the classical Bochner-Krall problem asking which linear ordinary differential operators possess sequences of eigenpolynomials s…
Level crossing in random matrices. II Random perturbation of a random matrix
Tobias Grøsfjeld, Boris Shapiro, Konstantin Zarembo
In this paper we study the distribution of level crossings for the spectra of linear families A+lambda B, where A and B are square matrices independently chosen from some given Gau…
Asymptotics and monodromy of the algebraic spectrum of quasi-exactly solvable sextic oscillator
Boris Shapiro, Milos Tater
Below we study theoretically and numerically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic potential, its level crossing points, and i…
Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix
B. Shapiro, K. Zarembo
We consider level crossing in a matrix family where is a fixed matrix and belongs to one of the standard Gaussian random matrix ensembles. We study…
Algebro-gemetric aspects of Heine-Stieltjes theory
Boris Shapiro
The goal of this paper is to develop a Heine-Stieltjes theory for univariate linear differential operators of higher order. Namely, for a given given operator T=\sum_i Q_i(z)d^i/dz…