6 citations · 19 across the 12 of their papers we have counts for
13 papers
The full shadow of a polynomial I. The limiting core and the transient set
Christian Hägg, Boris Shapiro
The full shadow of a complex polynomial of degree is the closure of all zeros of , , . We prove that it consists of a compact connected l…
Zero asymptotics for successive derivatives of hyperexponential functions with finite essential singularities
Christian Hägg, Boris Shapiro
Pólya's shire theorem identifies the final set of zeros of successive derivatives of an arbitrary meromorphic function with at least one pole with the Voronoi diagram of its finite…
Level Crossing in Random Matrices. III. Analogs of Girko's circular and Wigner's semicircle laws
B. Shapiro
We study the asymptotic distribution of level crossings for random matrix pencils A_n+λB_n in several ensembles, including complex and real i.i.d. matrices and Gaussian/Hermitian s…
A tropical analog of Descartes' rule of signs
J. Forsgård, D. Novikov, B. Shapiro
We prove that for any degree d, there exist (families of) finite sequences a_0, a_1,..., a_d of positive numbers such that, for any real polynomial P of degree d, the number of its…
On asymptotic Gauss-Lucas theorem
R. Boegvad, D. Khavinson, B. Shapiro
In this note we extend the Gauss-Lucas theorem on the zeros of the derivative of a univariate polynomial to the case of sequences of univariate polynomials whose almost all zeros l…
Elements of Polya-Schur theory in finite difference setting
P. Brändén, I. Krasikov, B. Shapiro
In this note we attempt to develop an analog of Pólya-Schur theory describing the class of univariate hyperbolicity preservers in the setting of linear finite difference operators.…