16 citations · 33 across the 11 of their papers we have counts for
18 papers
Decomposable Blaschke products of degree
Asuman Güven Aksoy, Francesca Arici, M. Eugenia Celorrio +1
We study the decomposability of a finite Blaschke product of degree into degree- Blaschke products, examining the connections between Blaschke products, the ellipt…
Blaschke Products, Level Sets, and Crouzeix's Conjecture
Kelly Bickel, Pamela Gorkin
We study several problems motivated by Crouzeix's conjecture, which we consider in the special setting of model spaces and compressions of the shift with finite Blaschke products a…
Interpolation in Model Spaces
Pamela Gorkin, Brett D. Wick
In this paper we consider interpolation in model spaces, with a Blaschke product. We study unions of interpolating sequences for two sequences that are far…
Crouzeix's Conjecture and related problems
Kelly Bickel, Pamela Gorkin, Anne Greenbaum +3
In this paper, we establish several results related to Crouzeix's conjecture. We show that the conjecture holds for contractions with eigenvalues that are sufficiently well-separat…
Numerical Range and Compressions of the Shift
Kelly Bickel, Pamela Gorkin
The numerical range of a bounded, linear operator on a Hilbert space is a set in that encodes important information about the operator. In this survey paper, we first…
Applications of Envelopes
Kelly Bickel, Pamela Gorkin, Trung Tran
Intuitively, an envelope of a family of curves is a curve that is tangent to a member of the family at each point. Here we use envelopes of families of circles to study objects fro…
Norms of truncated Toeplitz operators and numerical radii of restricted shifts
Pamela Gorkin, Jonathan R. Partington
This paper gives a new approach to the calculation of the numerical radius of a restricted shift operator by linking it to the norm of a truncated Toeplitz operator (TTO), which ca…
Compressions of the Shift on the Bidisk and their Numerical Ranges
Kelly Bickel, Pamela Gorkin
We consider two-variable model spaces associated to rational inner functions on the bidisk, which always possess canonical -invariant subspaces A particul…
Thin Sequences
Pamela Gorkin, Brett. D. Wick
We look at thin interpolating sequences and the role they play in uniform algebras, Hardy spaces, and model spaces.
Inner functions and operator theory
Isabelle Chalendar, Pamela Gorkin, Jonathan R. Partington
This tutorial paper presents a survey of results, both classical and new, linking inner functions and operator theory. Topics discussed include invariant subspaces, universal opera…
Thin Sequences and Their Role in Model Spaces and Douglas Algebras
Pamela Gorkin, Brett D. Wick
We study thin interpolating sequences and their relationship to interpolation in the Hardy space and the model spaces , where is an inner…
Thin sequences and the Gram matrix
Pamela Gorkin, Sandra Pott, John E. McCarthy +1
We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a com…
Thin Sequences and Their Role in Theory, Model Spaces, and Uniform Algebras
Pamela Gorkin, Sandra Pott, Brett D. Wick
In this paper we revisit some facts about thin interpolating sequences in the unit disc from three perspectives: uniform algebras, model spaces, and spaces. We extend the not…
The group of invariants of an inner function with finite spectrum
Isabelle Chalendar, Pamela Gorkin, Jonathan R. Partington
This paper determines the group of continuous invariants corresponding to an inner function with finitely many singularities on the unit circle ; that is, the continuous ma…
Numerical ranges of contractions
Chafiq Benhida, Pamela Gorkin, Dan Timotin
A conjecture of Halmos proved by Choi and Li states that the closure of the numerical range of a contraction on a Hilbert space is the intersection of the closure of the numerical…
Pervasive Algebras and Maximal Subalgebras
Pamela Gorkin, Anthony G. O'Farrell
A uniform algebra on its Shilov boundary is {\em maximal} if is not and there is no uniform algebra properly contained between and . It is {\em essenti…
Orbits of non-elliptic disc automorphisms
Eva A. Gallardo-Gutiérrez, Pamela Gorkin, Daniel Suárez
Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace generated by the limit points in the norm of the orbit of a thin Blaschke produc…
Approximation by polynomials and Blaschke products having all zeros on a circle
David W. Farmer, Pamela Gorkin
We show that a nonvanishing analytic function on a domain in the unit disc can be approximated by (a scalar multiple of) a Blaschke product whose zeros lie on a prescribed circle e…