On Random Polynomials Spanned By Opuc

Hanan Aljubran, Purdue University

Abstract

Aljubran, Hanan A. Ph.D., Purdue University, December 2020. On Random Polynomials Spanned by OPUC. Major Professor: Maxim L.Yattselev as n → ∞, where m is a non-negative integer (most of the work deal with the case m = 0 ), {ηn} ∞ n=0 is a sequence of i.i.d. Gaussian random variables, and {ϕn(z)} ∞ n=0 is a sequence of orthonormal polynomials on the unit circle T for some Borel measure µ on T with infinitely many points in its support. Most of the work is done by manipulating the density function for the expected number of zeros of a random polynomial, which we call the intensity function.

Degree

Ph.D.

Advisors

Yattselev, Purdue University.

Subject Area

Mathematics

COinS