Zobrazeno 1 - 10
of 147
pro vyhledávání: '"Simanek, Brian"'
Autor:
Reinhart, Graeme, Simanek, Brian
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 phenomenon that involves orthogonal polynomials on the unit circle. In the ca
Externí odkaz:
http://arxiv.org/abs/2408.06472
Autor:
Simanek, Brian, Wellman, Richard
We show that under very mild conditions on a measure $\mu$ on the real line, the span of $\{x^n\}_{n=j}^{\infty}$ is dense in $L^2(\mu)$ for any $j\in\mathbb{N}$. We also present a slightly weaker result with an interesting proof that uses Sobolev or
Externí odkaz:
http://arxiv.org/abs/2406.18353
Autor:
Simanek, Brian
We resolve some questions posed by Handelman in 1996 concerning log convex integrable functions. In particular, we give a negative answer to a question he posed concerning the integrability of $h^2(x)/h(2x)$ when $h$ is integrable and log convex and
Externí odkaz:
http://arxiv.org/abs/2402.10970
Autor:
Kraus, Adam, Simanek, Brian
Publikováno v:
Analysis and Mathematical Physics 14 (2024), no. 5
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 calculate the projection of $\bar{z}$ to the Bergman space of the bounded reg
Externí odkaz:
http://arxiv.org/abs/2312.12603
Autor:
Kraus, Adam, Simanek, Brian
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 problems that are analogous to Polya's conjecture for torsional rigidity of
Externí odkaz:
http://arxiv.org/abs/2309.16450
Autor:
Revilla, Nicole, Simanek, Brian
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 $\varphi(z)=z^{n}|z|^{2s}+a(t)\bar{z}^{m}|z|^{2t}$, where $s$ and $t$ are posi
Externí odkaz:
http://arxiv.org/abs/2211.00760
Autor:
Handley, Hunter, Simanek, Brian
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 periodic part of the sequence of continued fraction coefficients is doubly pa
Externí odkaz:
http://arxiv.org/abs/2205.06653
Autor:
Simanek, Brian
Publikováno v:
SIGMA 18 (2022), 047, 16 pages
We present determinantal formulas for families of exceptional $X_m$-Laguerre and exceptional $X_m$-Jacobi polynomials and also for exceptional $X_2$-Hermite polynomials. The formulas resemble Vandermonde determinants and use the zeros of the classica
Externí odkaz:
http://arxiv.org/abs/2202.01278
We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel-Darboux ke
Externí odkaz:
http://arxiv.org/abs/2108.01629
Given a natural number $n\geq3$ and two points $a$ and $b$ in the unit disk $\mathbb D$ in the complex plane, it is known that there exists a unique elliptical disk having $a$ and $b$ as foci that can also be realized as the intersection of a collect
Externí odkaz:
http://arxiv.org/abs/2101.12638