124 citations · 735 across the 42 of their papers we have counts for
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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.…
Hyperbolicity preservers and majorization
Julius Borcea, Petter Brändén
The majorization order on $\RR^n$ induces a natural partial ordering on the space of univariate hyperbolic polynomials of degree . We characterize all linear operators on polyno…
A generalization of the Heine--Stieltjes theorem
Petter Brändén
We extend the Heine-Stieltjes Theorem to concern all (non-degenerate) differential operators preserving the property of having only real zeros. This solves a conjecture of B. Shapi…
Multivariate Polya-Schur classification problems in the Weyl algebra
Julius Borcea, Petter Brändén
A multivariate polynomial is {\em stable} if it is nonvanishing whenever all variables have positive imaginary parts. We classify all linear partial differential operators in the W…