Prof. Aaron MELMAN, PhD., Department of Applied Mathematics, School of Engineering, Santa Clara University, USA: Recent Extensions of Some Polynomial Properties

În data de 10 septembrie 2022, ora 11:30, sala e (clădirea Mathematica), va avea loc prelegerea invitată cu titlul

Recent Extensions of Some Polynomial Properties

susținută de Prof. Aaron Melman, PhD., Santa Clara University, USA.


Several extensions of existing results for scalar polynomials are presented. The first concerns a directional version of Pellet's theorem, which establishes an exclusion interval for the magnitudes of the zeros of a scalar polynomial having a given argument. Subsequent extensions involve real polynomials with sign restrictions on their coefficients. The first of these is an improvement of theorems of Hayashi and Hurwitz that describe properties of the nonreal zeros of such polynomials, while a second extension widens an exclusion sector for their zeros. To conclude, it is shown how some of the above results can be generalized to matrix polynomials, and how scalar and matrix polynomial features can be combined to produce further results.