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
My CV

Research

I am interested in operator theory, complex analysis,
polynomial zero sets and sums of squares decompositions,
and harmonic analysis.

Grants

NSF analysis grant 2019-2022 Operator theory and stable polynomials

NSF analysis grant 2014-2018 Harmonic analysis and spaces of analytic functions in several variables

NSF analysis grant 2010-2014: "Operator related function theory and algebraic varieties"

Papers

On arXiv and MathSciNet

  1. Kummert’s approach to realization on the bidisk Submitted 2019.
  2. (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.
  3. Global bounds on stable polynomials , Complex Anal. Oper. Theory 13 (2019), no. 4, 1895-1915. DOI
  4. Extreme points and saturated polynomials. Illinois J. Math. 63 (2019), no. 1, 47-74.
  5. (with Kosinski, Ransford, and Sola) Cyclic polynomials in anisotropic Dirichlet spaces , to appear in Journal d'Analyse.
  6. The von Neumann inequality for 3x3 matrices , Bull. Lond. Math. Soc. 48 (2016), no. 1, 53-57.
  7. Integrability and regularity of rational functions , Proc. Lond. Math. Soc. (3) 111 (2015), no. 6, 1261-1306.
  8. (with Beneteau, Kosinski, Liaw, Seco, and Sola) Cyclic polynomials in two variables , Trans. Amer. Math. Soc. 368 (2016), no. 12, 8737-8754.
  9. (with K. Bickel) Canonical Agler decompositions and transfer function realizations , Trans. Amer. Math. Soc. 368 (2016), no. 9, 6293-6324.
  10. Determinantal representations of semi-hyperbolic polynomials , Michigan Math. J. 65 (2016), no. 3, 473-487.
  11. (with J. McCarthy and K. Moen) Unions of Lebesgue spaces and A_1 majorants , Pacific J. Math. 280 (2016), no. 2, 411-432.
  12. (with J. Geronimo and P. Iliev) Polynomials with no zeros on a face of the bidisk , J. Funct. Anal. 270 (2016), no. 9, 3505-3558.
  13. (with P.M. Gauthier) Zero-free polynomial approximation on a chain of Jordan domains , Ann. Sci. Math. Qu\'ebec 36 (2012), no.1, 107-112.
  14. (with K. Bickel) Inner functions on the bidisk and associated Hilbert spaces , J. Funct. Anal. 265 (2013), no. 11, 2753-2790.
  15. Uchiyama's lemma and the John-Nirenberg inequality , Bull. Lond. Math. Soc. 45 (2013), no. 4, 683-692.
  16. (with J. Geronimo and P. Iliev) 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, 2012. Also here
  17. Schur-Agler class rational inner functions on the tridisk , Proc. Amer. Math. Soc., 139(2011), 4063-4072. Also here .
  18. A refined Agler decomposition and geometric applications , Indiana Univ. Math. J. 60 (2011), 1831-1842. Also here
  19. (with M. Jury and S. McCullough) Nevanlinna-Pick interpolation on distinguished varieties in the bidisk , 2012, J. Functional Analysis, 262(9), 3812-3838.
  20. Stable symmetric polynomials and the Schur-Agler class , Illinois J. Math. 55 (2011), no. 4, 1603-1620 (2013).
  21. Rational inner functions in the Schur-Agler class of the polydisk , 2011, Publ. Mat., 55(2), 343-357.
  22. Kernel decompositions for Schur functions on the polydisk, 2011, Complex Analysis and Operator Theory, 5(4), 1093-1111.
  23. Polynomials with no zeros on the bidisk, , Analysis and PDE, Vol. 3 (2010) No. 2, 109-149.
  24. Polynomials defining distinguished varieties, 2010, Trans. Math. Amer. Soc., 362(11), 5635-5655.
  25. (with M.Jury and S.McCullough) Agler interpolation families of kernels, 14 pages,
    Operators and Matrices, Vol. 3 (2009) No. 4, 571-587.
  26. (with J. Agler and J. McCarthy) Algebraic pairs of isometries, 2012, J. Operator Theory, 67(1), 215-236. Also here .
  27. Bernstein-Szegõ measures on the two dimensional torus, Indiana Univ. Math. J. 57 No. 3 (2008), 1353-1376. Also here .
  28. Function theory on the Neil parabola, Michigan Math. J., Vol. 55, Issue 1 (2007), 139-154.
  29. A Schwarz lemma on the polydisk, Proc. Amer. Math. Soc., 135 (2007), 2759-2768.

Teaching

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 Fall 2015
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
Older teaching

Other things

IWOTA 2016
Operator theory and the singular value decomposition Oberwolfach snapshot.
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 videos
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.
My math genealogy