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pro vyhledávání: '"Knese, Greg"'
Autor:
Knese, Greg
This article examines three radii associated to bounded analytic functions on the polydisk: the well-known Bohr radius, the Bohr-Agler radius, and the Schur-Agler radius. We prove explicit upper and lower bounds for the Bohr-Agler radius, an explicit
Externí odkaz:
http://arxiv.org/abs/2410.21693
Autor:
Knese, Greg
Rational inner functions are a generalization of finite Blaschke products to several variables. In this article we survey a variety of results about rational inner functions related to interpolation, sums of squares formulas, and boundary behavior. W
Externí odkaz:
http://arxiv.org/abs/2409.14604
Given a polynomial $p$ with no zeros in the polydisk, or equivalently the poly-upper half-plane, we study the problem of determining the ideal of polynomials $q$ with the property that the rational function $q/p$ is bounded near a boundary zero of $p
Externí odkaz:
http://arxiv.org/abs/2406.13014
Autor:
Knese, Greg
Motivated by studying boundary singularities of rational functions in two variables that are analytic on a domain, we investigate local integrability on $\mathbb{R}^2$ near $(0,0)$ of rational functions with denominator non-vanishing in the bi-upper
Externí odkaz:
http://arxiv.org/abs/2404.05042
We provide detailed local descriptions of stable polynomials in terms of their homogeneous decompositions, Puiseux expansions, and transfer function realizations. We use this theory to first prove that bounded rational functions on the polydisk posse
Externí odkaz:
http://arxiv.org/abs/2109.07507
Autor:
Knese, Greg
Publikováno v:
Proc. Amer. Math. Soc. 148 (2020), no. 8, 3453-3456
A short and simple proof of necessity in the McCullough-Quiggin characterization of positive semi-definite kernels with the complete Pick property is presented.
Externí odkaz:
http://arxiv.org/abs/1912.13068
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Autor:
Knese, Greg
Publikováno v:
Indiana Univ. Math. J. 70 (2021), no. 6, 2369-2403
We give a simplified exposition of Kummert's approach to proving that every matrix-valued rational inner function in two variables has a minimal unitary transfer function realization. A slight modification of the approach extends to rational function
Externí odkaz:
http://arxiv.org/abs/1907.13191
Autor:
Knese, Erin Darnell, Keel, William C., Knese, Greg, Bennert, Vardha N., Moiseev, Alexei, Grokhovskaya, Aleksandra, Dodonov, Sergei N.
Publikováno v:
Monthly Notices of the Royal Astronomical Society, Volume 496 (2020), Issue 2, pp.1035-1050
Motivated by the discovery of large-scale ionized clouds around AGN host galaxies, and particularly the large fraction of those which are consistent with photoionized gaseous tidal debris, we have searched for [O III] emission over wide fields around
Externí odkaz:
http://arxiv.org/abs/1905.12693
Autor:
Knese, Greg
Publikováno v:
Complex Anal. Oper. Theory 13 (2019), no. 4, 1895--1915
A classical inequality of Sz\'asz bounds polynomials with no zeros in the upper half plane entirely in terms of their first few coefficients. Borcea-Br\"and\'en generalized this result to several variables as a piece of their characterization of line
Externí odkaz:
http://arxiv.org/abs/1708.01699