57 citations · 275 across the 73 of their papers we have counts for
23 papers · 1 filter
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…
Finiteness of rank for Grassmann convexity
Nicolau C. Saldanha, Boris Shapiro, Michael Shapiro
The Grassmann convexity conjecture gives a conjectural formula for the maximal total number of real zeros of the consecutive Wronskians of an arbitrary fundamental solution to a di…
Rodrigues' descendants of a polynomial and Boutroux curves
Rikard Bøgvad, Christian Hägg, Boris Shapiro
Motivated by the classical Rodrigues' formula, we study the root asymptotic of the polynomial sequence where ${P(…
Generalizing Tran's Conjecture
Rikard Bögvad, Innocent Ndikubwayo, Boris Shapiro
A conjecture of Khang Tran [6] claims that for an arbitrary pair of polynomials and , every zero of every polynomial in the sequence satisfyi…
Grassmann convexity and multiplicative Sturm theory, revisited
Nicolau Saldanha, Boris Shapiro, Michael Shapiro
In this paper we settle a special case of the Grassmann convexity conjecture formulated earlier by B.and M.Shapiro. We present a conjectural formula for the maximal total number of…
New aspects of Descartes' rule of signs
Vladimir Petrov Kostov, Boris Zalmanovich Shapiro
Below we summarize some new developments in the area of distribution of roots and signs of real univariate polynomials pioneered by R.~Descartes in the middle of the 17-th century.