My main research interest lies in the study of the distribution of zeros of entire functions. More specifically, I study multiplier sequences of the first and second kind, as well as their alternate representation as linear operators on the ring R[x]. This work has connections with the study of special functions, including the special orthogonal polynomials of Hermite, Laguerre, Legendre and Chebyshev; Bessel functions, and generalized hypergeometric functions. Real entire functions in general play a central role in my research, specifically those belonging to the Laguerre-Pólya class. The problem of understanding the relationship between functions in this class, and the class of functions which interpolate multiplier sequences of various kinds had long been open, and continues to attract research interest, including mine.
In the recent years I have also been involved in research projects investigating the kinds of functions which generate a sequence of polynomials, all of which are hyperbolic. Prof. Khang Tran and I have studied rational functions with a binomial type denominator, as well as rational functions with hyperbolic type denominators. We are currently working on understanding generating functions with transcendental denominators.
I am always looking for interested students to work on research projects with me. In the recent years I have mentored 20 undergraduate students in various research projects, 10 of whom are coauthors of mine on research publications. These students have given numerous conference presentations, both oral and poster, and many of them have gone on to graduate programs around the nation.