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pro vyhledávání: '"Gorkin, Pamela"'
We study the decomposability of a finite Blaschke product $B$ of degree $2^n$ into $n$ degree-$2$ Blaschke products, examining the connections between Blaschke products, the elliptical range theorem, Poncelet theorem, and the monodromy group. We show
Externí odkaz:
http://arxiv.org/abs/2206.07466
Autor:
Bickel, Kelly, Gorkin, Pamela
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 as symbols. We pose a version of the conjecture in this setting, called
Externí odkaz:
http://arxiv.org/abs/2112.06321
Autor:
Gorkin, Pamela, Wick, Brett D.
In this paper we consider interpolation in model spaces, $H^2 \ominus B H^2$ with $B$ a Blaschke product. We study unions of interpolating sequences for two sequences that are far from each other in the pseudohyperbolic metric as well as two sequence
Externí odkaz:
http://arxiv.org/abs/2009.01957
Autor:
Bickel, Kelly, Gorkin, Pamela, Greenbaum, Anne, Ransford, Thomas, Schwenninger, Felix, Wegert, Elias
Publikováno v:
Comput. Methods Funct. Theory, 2020
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-separated. This separation is measured by the so-called separation constant,
Externí odkaz:
http://arxiv.org/abs/2006.04901
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 from matrix theory and hyperbolic geometry. First we explore relationship
Externí odkaz:
http://arxiv.org/abs/1810.11678
Autor:
Bickel, Kelly, Gorkin, Pamela
The numerical range of a bounded, linear operator on a Hilbert space is a set in $\mathbb{C}$ that encodes important information about the operator. In this survey paper, we first consider numerical ranges of matrices and discuss several connections
Externí odkaz:
http://arxiv.org/abs/1810.11680
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 can be be calculated by various methods. Further results on the norm of
Externí odkaz:
http://arxiv.org/abs/1711.06042
Autor:
Bickel, Kelly, Gorkin, Pamela
We consider two-variable model spaces associated to rational inner functions $\Theta$ on the bidisk, which always possess canonical $z_2$-invariant subspaces $\mathcal{S}_2.$ A particularly interesting compression of the shift is the compression of m
Externí odkaz:
http://arxiv.org/abs/1702.05204
Akademický článek
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Autor:
Adams, Gregory, Gorkin, Pamela
Publikováno v:
In Journal of Functional Analysis 15 October 2021 281(8)
