Professor

Analysis, functional analysis

PhD, University of Michigan

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, "Complex FIO's and composition of Toeplitz operators," arXiv 2205.08649 [math FA].
- L. A. Coburn, "Approximation by Lipschitz functions," arXiv: 2104.13153 [math FA].
- L. A. Coburn, M. Hitrik , J. Sjoestrand and F. White, "Weyl symbols and boundedness of Toeplitz operators,"
*Mathematical Research Letters,*28 (2021) pp. 681-696. - 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.