4 papers · 1 filter
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…
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…