Greg Knese's Home Page
I'm an Associate Professor at Washington University in St. Louis.
I was previously at the University of Alabama (2010-2013) and UC Irvine (2007-2010).
You can email me at geknese shift2 wustl dot edu.
My office is 214 Cupples I
I am interested in operator theory, complex analysis,
polynomial zero sets and sums of squares decompositions,
and harmonic analysis.
NSF analysis grant 2019-2022 Operator theory and stable polynomials
analysis grant 2014-2018 Harmonic analysis and spaces of analytic
functions in several variables
analysis grant 2010-2014: "Operator related function theory and
- A simple proof of necessity in the McCullough-Quiggin theorem.
- Kummert’s approach to realization on the bidisk.
- (with E.D. Knese, Keel, Bennert, Moiseev, Grokhovskaya, Dodonov)
An [O III] search for extended emission around AGN with H I mapping:
a distant cloud ionized by Mkn 1 submitted 2019. Note: This is an astronomy paper with a spherical version
of the Buffon needle problem in the appendix.
- Global bounds on
stable polynomials ,
Complex Anal. Oper. Theory 13 (2019), no. 4, 1895-1915.
- Extreme points and
saturated polynomials. Illinois J. Math. 63 (2019), no. 1, 47-74.
- (with Kosinski, Ransford, and Sola) Cyclic
polynomials in anisotropic Dirichlet spaces , to appear in
- The von
Neumann inequality for 3x3 matrices , Bull. Lond. Math. Soc. 48 (2016), no. 1, 53-57.
Integrability and regularity of rational functions , Proc. Lond. Math. Soc. (3) 111 (2015), no. 6, 1261-1306.
- (with Beneteau, Kosinski, Liaw, Seco, and Sola) Cyclic polynomials
in two variables , Trans. Amer. Math. Soc. 368 (2016), no. 12, 8737-8754.
- (with K. Bickel)
Canonical Agler decompositions and transfer function realizations
, Trans. Amer. Math. Soc. 368 (2016), no. 9, 6293-6324.
- Determinantal representations
of semi-hyperbolic polynomials ,
Michigan Math. J. 65 (2016), no. 3, 473-487.
- (with J. McCarthy and K. Moen) Unions of Lebesgue
spaces and A_1 majorants , Pacific J. Math. 280 (2016), no. 2, 411-432.
- (with J. Geronimo and
Polynomials with no zeros on a face of the bidisk ,
J. Funct. Anal. 270 (2016), no. 9, 3505-3558.
Zero-free polynomial approximation on a chain of Jordan
domains , Ann. Sci. Math. Qu\'ebec 36 (2012), no.1, 107-112.
K. Bickel) Inner
functions on the bidisk and associated Hilbert spaces ,
J. Funct. Anal. 265 (2013), no. 11, 2753-2790.
Uchiyama's lemma and the John-Nirenberg inequality ,
Bull. Lond. Math. Soc. 45 (2013), no. 4, 683-692.
- (with J. Geronimo and
Orthogonality relations for bivariate Bernstein-Szego
measures , Recent advances in orthogonal polynomials, special
functions, and their applications, 119-131, Contemp. Math., 578,
Amer. Math. Soc., Providence, RI,
Schur-Agler class rational inner functions on the tridisk ,
Proc. Amer. Math. Soc., 139(2011), 4063-4072. Also
- A refined
Agler decomposition and geometric applications , Indiana
Univ. Math. J. 60 (2011),
- (with M. Jury and S. McCullough)
Nevanlinna-Pick interpolation on distinguished varieties in the
bidisk , 2012, J. Functional Analysis, 262(9), 3812-3838.
Stable symmetric polynomials and the Schur-Agler class , Illinois
J. Math. 55 (2011), no. 4, 1603-1620 (2013).
Rational inner functions in the Schur-Agler class of the
polydisk , 2011, Publ. Mat., 55(2), 343-357.
Kernel decompositions for Schur functions on the polydisk,
2011, Complex Analysis and Operator Theory, 5(4),
Polynomials with no zeros on the bidisk, , Analysis and PDE, Vol. 3 (2010) No. 2, 109-149.
Polynomials defining distinguished varieties, 2010,
Trans. Math. Amer. Soc., 362(11), 5635-5655.
- (with M.Jury and S.McCullough) Agler
interpolation families of kernels, 14 pages,
Operators and Matrices, Vol. 3 (2009) No. 4, 571-587.
- (with J. Agler and
J. McCarthy) Algebraic
pairs of isometries, 2012, J. Operator
Theory, 67(1), 215-236. Also
- Bernstein-Szegõ measures on the two
dimensional torus, Indiana Univ. Math. J. 57 No. 3 (2008),
- Function theory on the Neil
parabola, Michigan Math. J., Vol. 55, Issue 1 (2007),
- A Schwarz lemma on the polydisk,
Proc. Amer. Math. Soc., 135 (2007), 2759-2768.
Topics course on Reproducing kernel Hilbert space, Spring 2019
Partial Differential Equations, Math 415, Fall 2018
Analytic Combinatorics, Math 470, Fall 2018
Function theory on the polydisk, Math 522, Spring 2018
Measure Theory and Functional Analysis II Math 5052 Spring 2018
Measure Theory and Functional Analysis I Math 5051 Fall 2017
Measure Theory and Functional Analysis II Math 5052 Spring 2017
Geometry I Math 5041 Fall 2016
Calculus of Several Variables Math 318 Spring 2016
Complex Analysis II Math 5022 Spring 2016
Complex Analysis I Math 5021
Measure theory and functional analysis II Math 5052 Spring 2015
Measure theory and functional analysis I Math 5051 Fall 2014
Matrix Algebra Math 309 Fall 2013
Operator theory and the singular value decomposition Oberwolfach
Slides from AMS/MAA joint
meetings in San Diego January 2013.
Texas A and M 2012 slides on Uchiyama's lemma
IWOTA 2012 slides on Distinguished Varieties
Slides from SEAM 27.
Richmond AMS meeting slides.
My Youtube calculus
Slides and audio for the presentation "Rational inner functions
on the bidisk" presented at the Fields institute.
LaTeX style file , metafont file , and
user's guide to a font/notation I
created for two of the above papers.