NEW MULTIPLIER SEQUENCES VIA DISCRIMINANT AMOEBAE Academic Article uri icon

abstract

  • In their classic 1914 paper, Polya and Schur introduced and characterized two types of linear operators acting diagonally on the monomial basis of R[ai], 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. 2011 Independent University of Moscow.

published proceedings

  • MOSCOW MATHEMATICAL JOURNAL

author list (cited authors)

  • Passare, M., Rojas, J. M., & Shapiro, B.

complete list of authors

  • Passare, Mikael||Rojas, J Maurice||Shapiro, Boris

publication date

  • August 2011