23 citations · 74 across the 30 of their papers we have counts for
37 papers
Upper bounds on eigenvalue spacing for decaying potentials
Milivoje Lukic, Brian Simanek
We study decaying half-line Schrödinger operators and the local eigenvalue spacing of their Dirichlet restrictions. While absolutely continuous spectrum is strongly associated with…
Orthogonal Polynomials on the Unit Circle, Mutually Unbiased Bases, and Balanced States
Graeme Reinhart, Brian Simanek
Two interesting phenomena for the construction of quantum states are that of mutually unbiased bases and that of balanced states. We explore a constructive approach to each phenome…
Bounded Connected Components of Polynomial Lemniscates
Adam Kraus, Brian Simanek
We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calcula…
New Perspectives on Torsional Rigidity and Polynomial Approximations of z-bar
Adam Kraus, Brian Simanek
We consider polynomial approximations of z-bar to better understand the torsional rigidity of polygons. Our main focus is on low degree approximations and associated extremal probl…
Hyponormal Toeplitz Operators on the Bergman Space of the Disk
Nicole Revilla, Brian Simanek
We consider Toeplitz operators with bounded symbol acting on the Bergman space of the unit disk and assess their hyponormality. We will mainly be concerned with the symbol $φ(z)=z^…
Discrete m-functions with Doubly Palindromic Continued Fraction Coefficients
Hunter Handley, Brian Simanek
We demonstrate that discrete m-functions with eventually periodic continued fraction coefficients have an algebraic relationship to their second solution if and only if the periodi…