6 papers · 1 filter
Monotonicity of the principal pivot transform
J. E. Pascoe, Ryan Tully-Doyle
We prove that the principal pivot transform (also known as the partial inverse, sweep operator, or exchange operator in various contexts) maps matrices with positive imaginary part…
Analytic continuation of concrete realizations and the McCarthy Champagne conjecture
Kelly Bickel, J. E. Pascoe, Ryan Tully-Doyle
In this paper, we give formulas that allow one to move between transfer function type realizations of multi-variate Schur, Herglotz and Pick functions, without adding additional si…
Automatic real analyticity and a regal proof of a commutative multivariate Löwner theorem
J. E. Pascoe, Ryan Tully-Doyle
We adapt the "royal road" method used to simplify automatic analyticity theorems in noncommutative function theory to several complex variables. We show that certain families of fu…
The royal road to automatic noncommutative real analyticity, monotonicity, and convexity
J. E. Pascoe, Ryan Tully-Doyle
It was shown classically that matrix monotone and matrix convex functions must be real analytic by Löwner and Kraus respectively. Recently, various analogues have been found in sev…
Escaping nontangentiality: Towards a controlled tangential amortized Julia-Carathéodory theory
J. E. Pascoe, Meredith Sargent, Ryan Tully-Doyle
Let be a complex analytic function. The Julia quotient is given by the ratio between the distance of to the boundary of and the distance of to t…
Analytic functions on the bidisk at boundary singularities via Hilbert space methods
Ryan Tully-Doyle
We investigate the behavior of a generalized Hilbert space model of a function in the Schur class of the bidisk at singular boundary points that satisfy a growth condition. We exam…