57 citations · 275 across the 73 of their papers we have counts for
4 papers · 1 filter
On eigenvalues of rectangular matrices
Julius Borcea, Boris Shapiro, Michael Shapiro
Given a -tuple of -matrices with we call the set of all -tuples of complex numbers $\{\la_1,...,\la_k\}$ such that the linear combi…
Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions
Julius Borcea, Rikard Bøgvad, Boris Shapiro
Consider a homogenized spectral pencil of exactly solvable linear differential operators $T_{\la}=\sum_{i=0}^k Q_{i}(z)\la^{k-i}\frac {d^i}{dz^i}$, where each is a polyn…
Spaces of locally convex curves in S^n and combinatorics of the group B_{n+1}
Nicolau C. Saldanha, Boris Shapiro
In the 1920's Marston Morse developed what is now known as Morse theory trying to study the topology of the space of closed curves on S^2. We propose to attack a very similar probl…
Root asymptotics of spectral polynomials for the Lame operator
Julius Borcea, Boris Shapiro
The study of polynomial solutions to the classical Lamé equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Su…