Professor

PhD, University of Michigan

**Contact Information: 327 Mathematics Building University at Buffalo Buffalo, NY 14260-2900**

Tel: (716) 645-8813

Fax: (716) 645-5039

E-mail: lcoburn@buffalo.edu

Personal website: Lewis Coburn

**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.

L. A. Coburn, M. Hitrik and J. Sjoestrand, ``Positivity, complex FIOs, and Toeplitz operators," accepted for publication in * Pure and Applied Mathematics.*

L. A. Coburn, ``Fock space, the Heisenberg group, heat flow and Toeplitz operators," to appear as chapter 1 in *Analytic function spaces and operators on them, * ed. Kehe Zhu, CRC Press.

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.