13 citations · 26 across the 19 of their papers we have counts for
19 papers
Automorphic Nelson Dilations for Contractions and Invariant Subspace Tracking
Kelly Bickel, J. E. Pascoe, Ryan Tully-Doyle
Given an strictly contractive matrix , an (automorphic) Nelson dilation of is a certain type of analytic matrix-valued function on the unit disk w…
Cauchy Transforms of Colored Graphs in Two Variables
Lily Adlin, Giovani Thai, Samuel Tiscareno +1
By designating vertices with variables, a simple undirected graph can be augmented to have an associated representing rational function in two variables taking the complex bi-upper…
Matrix convex verbatim enumeration functions are graphical
J. E. Pascoe, Ryan Tully-Doyle
We give a relation between verbatim generating functions of what we call Pythagorean languages and matrix convexity. Namely, several multivariate matrix convex functions occurring…
Induced Stinespring factorization and the Wittstock support theorem
J. E. Pascoe, Ryan Tully-Doyle
Given a pair of self-adjoint-preserving completely bounded maps on the same -algebra, say that if the kernel of is a subset of the kernel of and $ψ\circ φ^{-…
Dynamics of low-degree rational inner skew-products on
Alan Sola, Ryan Tully-Doyle
We examine iteration of certain skew-products on the bidisk whose components are rational inner functions, with emphasis on simple maps of the form …
Averaged mixed Julia-Fatou type theory with applications to spectral foliation
J. E. Pascoe, Ryan Tully-Doyle
Classically, theorems of Fatou and Julia describe the boundary regularity of functions in one complex variable. The former says that a complex analytic function on the disk has non…
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…
Cauchy transforms arising from homomorphic conditional expectations parametrize free Pick functions but those arising from conditional expectations do not
J. E. Pascoe, Ryan Tully-Doyle
Nevanlinna showed that Cauchy transforms of probability measures parametrize all functions from the upper half plane into itself satisfying a certain asymptotic condition at infini…
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…
Representation of free Herglotz functions
J. E. Pascoe, Benjamin Passer, Ryan Tully-Doyle
A Herglotz function is a holomorphic map from the open complex unit disk into the closed complex right halfplane. A classical Herglotz function has an integral representation again…
Convex entire noncommutative functions are polynomials of degree two or less
J. William Helton, J. E. Pascoe, Ryan Tully-Doyle +1
This paper concerns matrix "convex" functions of (free) noncommuting variables, . Helton and McCullough showed that a polynomial in which is matrix conv…
Free functions with symmetry
David Cushing, J. E. Pascoe, Ryan Tully-Doyle
In 1936, Margarete C. Wolf showed that the ring of symmetric free polynomials in two or more variables is isomorphic to the ring of free polynomials in infinitely many variables. W…
Free Pick functions: representations, asymptotic behavior and matrix monotonicity in several noncommuting variables
J. E. Pascoe, Ryan Tully-Doyle
We extend the study of the Pick class, the set of complex analytic functions taking the upper half plane into itself, to the noncommutative setting. R. Nevanlinna showed that eleme…
Boundary behavior of analytic functions of two variables via generalized models
J. Agler, R. Tully-Doyle, N. J. Young
We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boun…
Nevanlinna representations in several variables
Jim Agler, R. Tully-Doyle, N. J. Young
We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imag…