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University of Alaska Southeast

Title: Diagonalizable Linear Operators and Polynomial Zeros

Directors: Andrzej Piotrowski

Email: apiotrowski@uas.alaska.edu

Dates of Program: May 13 - June 15, 2013

Summary:

This program will focus on open problems regarding the location of zeros of polynomials. This area of research has a rich history and it is important in many branches of mathematics, e.g., algebra, analysis, analytic number theory, differential equations, combinatorics, and probability. A main focus of the research project will pertain to classification problems for Q-multiplier sequences. That is to say, for a given basis Q = {q_0, q_1, q_2, . . . } for the vector space of real polynomials, we will attempt to characterize all sequences of real numbers {g_0, g_1, g_2, . . . } for which the linear operator T defined by T(q_k) = g_k * q_k (k=0, 1, 2, . . . ) maps every polynomial with only real zeros into another polynomial with only real zeros.

Student Researchers Supported by MAA:

Andre Bunton
Nicole (Niki) Jacobs
Samantha Jenkins
Charles McKenry Jr.
Louie Scott

Program Contacts:

Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473

Support for NREUP is provided by the National Science Foundation's Division of Mathematical Sciences and the National Security Agency.

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