|
This article is cited in 6 scientific papers (total in 6 papers)
New multiplier sequences via discriminant amoebae
Mikael Passarea, J. Maurice Rojasb, Boris Shapiroa a Department of Mathematics, Stockholm University, Stockholm, Sweden
b Department of Mathematics, Texas A&M University, College Station, Texas, USA
Abstract:
In their classic 1914 paper, Pólya and Schur introduced and characterized two types of linear operators acting diagonally on the monomial basis of $\mathbb R[x]$, sending real-rooted polynomials (resp. polynomials with all nonzero roots of the same sign) to real-rooted polynomials. Motivated by fundamental properties of amoebae and discriminants discovered by Gelfand, Kapranov, and Zelevinsky, we introduce two new natural classes of polynomials and describe diagonal operators preserving these new classes. A pleasant circumstance in our description is that these classes have a simple explicit description, one of them coinciding with the class of log-concave sequences.
Key words and phrases:
multiplier sequence, discriminant, amoeba, chamber.
Received: September 24, 2010
Citation:
Mikael Passare, J. Maurice Rojas, Boris Shapiro, “New multiplier sequences via discriminant amoebae”, Mosc. Math. J., 11:3 (2011), 547–560
Linking options:
https://www.mathnet.ru/eng/mmj432 https://www.mathnet.ru/eng/mmj/v11/i3/p547
|
|