57 citations · 275 across the 73 of their papers we have counts for
78 papers
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…
An inverse problem in Pólya--Schur theory. II. Exactly solvable operators and complex dynamics
Per Alexandersson, Nils Hemmingsson, Boris Shapiro
This paper, being the sequel of [An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators], studies a class of linear ordinary differential operators wi…
An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators
Per Alexandersson, Petter Brändén, Boris Shapiro
Given a linear ordinary differential operator T with polynomial coefficients, we study the class of closed subsets of the complex plane such that T sends any polynomial (resp. any…
Introducing isodynamic points for binary forms and their ratios
Christian Hägg, Boris Shapiro, Michael Shapiro
The isodynamic points of a plane triangle are known to be the only pair of its centers invariant under the action of the Mobius group on the set of triangles. Generalizing this cla…
Deformed graphical zonotopal algebras
Boris Shapiro, Ilya Smirnov, Arkady Vaintrob
We study certain filtered deformations of the external zonotopal algebra of a given graph parametrized by univariate polynomials. We establish some general properties of these alge…
Linear first order differential operators and their Hutchinson-invariant sets
Per Alexandersson, Nils Hemmingsson, Dmitry Novikov +2
In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in details in the simplest case of…