B.S. Mathematics, California Polytechnic State University, San Luis Obispo
Ph.D. Mathematics, University of California, San Diego
I am interested in the use of operator theoretic techniques to solve problems in functional analysis in several variables. In particular, I am interested in generalizing theorems of classical complex analysis concerning important families of analytic functions to the several variable case. I am also investigating functions in non-commuting variables with properties that make them natural on matrix inputs.
Pascoe, J. E. and R. Tully-Doyle. 2017. Free Pick functions: representations, asymptotic behavior, and matrix monotonicity. Journal of Functional Analysis. doi.org/10.1016/j.jfa.2017.04.001
Tully-Doyle, R. Analytic functions on the bidisk at boundary singularities via Hilbert space methods. 2016. Operators and Matrices. doi.org/10.7153/oam-11-04
Helton, J. W., J. E. Pascoe, R. Tully-Doyle, and V. Vinnikov. 2016. Convex entire noncommutative functions are polynomials of degree two or less. Integral Equations and Operator Theory. doi.org/10.1007/s00020-016-2317-y
Agler, J., R. Tully-Doyle, and N. J. Young. 2016. Nevanlinna representations in several variables. Journal of Functional Analysis. doi.org/10.1016/j.jfa.2016.02.004