Lewis A. Coburn

PhD

Lewis A. Coburn.

Lewis A. Coburn

PhD

Lewis A. Coburn

PhD

Research Interests

Analysis, functional analysis

Contact Information

327 Mathematics Building

UB North Campus

Buffalo NY, 14260-2900

Phone: (716) 645-8813

Fax: (716) 645-5039

lcoburn@buffalo.edu

Education

PhD, University of Michigan

Research Summary

Analysis, functional analysis

My research interests include operator theory, C*-algebras, and quantum mechanics from the viewpoint of deformations of C*-algebras. The operators on which I focus are usually of Toeplitz-type and act on the square-integrable holomorphic functions on phase-space.  I am interested in C*-algebras of these operators with various interesting "symbols" and the relation of such algebras to algebras of pseudo-differential operators which have been studied classically.

In the past several years, I have become interested in the structure of the Berezin symbol calculus of general operators on Bergman reproducing kernel Hilbert spaces. This calculus serves as a model for "quantization" and has been the object of considerable attention since it was introduced by Berezin in the 1970's.

Selected Publications

  • L. A. Coburn, M. Hitrik and J. Sjoestrand, “Positivity, complex FIOs, and Toeplitz operators,“Pure and Applied Analysis, 1 (2019) pp. 327-357.
  • L. A. Coburn, "Fock space, the Heisenberg group, heat flow and Toeplitz operators," chapter 1 (pp. 1 – 15) in Handbook of analytic operator theory, (ISBN 9781138486416), ed. Kehe Zhu, CRC Press, 2019.
  • W. Bauer, L. A. Coburn and R. Hagger, “Toeplitz quantization on Fock space,” Journal of Functional Analysis, 274 (2018) pp. 3531-3551.
  • W. Bauer and L. A. Coburn, “Uniformly continuous functions and quantization on the Fock space,”Bol. Soc. Mat. Mex., 22 (2016) pp. 669-677.
  • W. Bauer and L. A. Coburn, "Toeplitz operators with uniformly continuous symbols," Integral equations and operator theory 83 (2015) 24-34.
  • W. Bauer and L. A. Coburn, "Heat flow, weighted Bergman spaces and real-analytic Lipschitz approximation," J. reine angew. Math. 703 (2015) 225-246.
  • L. A. Coburn, "Berezin transform and Weyl-type unitary operators on the Bergman space," Proceedings of the AMS, 140 (2012) pp. 3445-3451.
  • L. A. Coburn, J. Isralowitz, and Bo Li, "Toeplitz operators with BMO symbols on the Segal-Bargmann space," Transactions of the AMS, 363 (2011) pp. 3015-3030.
  • W. Bauer, L. A. Coburn, and J. Isralowitz, "Heat flow, BMO and the compactness of Toeplitz operators", Journal of Functional Analysis 259 (2010)  pp. 57-78.
  • L. A. Coburn and Bo Li, "Directional derivative estimates for Berezin's operator calculus," Proceedings of the AMS 136 (2008) pp. 641-649.
  • L. A. Coburn, "Sharp Berezin Lipschitz estimates”, Proceedings of the AMS, 135 (2007) pp. 1163-1168.