Mathematical Sciences: Toeplitz Operators, Quantum Mechanicsand Mean Oscillation
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Professor Coburn will continue his study of the symbol                     calculus associated with the Berezin - Toeplitz quantization. One               specific setting is complex n-space with Gaussian measure, and                  with moderate growth and oscillation conditions on the                          singularities of the symbols. Coburn will seek to characterize                  bounded Hankel operators in this setting in terms of mean                       oscillation of symbols. The corresponding boundedness problem for               the Hardy spaces of the ball and polydisc will also be attacked.                Coburn expects the techniques developed in working on these                     problems to be useful in the study of derivations on various                    naturally occurring algebras.                                                        The impetus for this general area of mathematical research                 comes from quantum mechanics. In the classical, pre-quantum                     overview of the world, the observables of a physical system are                 numbers, or, if one wants to keep track of the dependency of                    these numbers on some other quantities, functions. This is common               sense, but at the microscopic level it doesn't quite work. One                  needs to replace functions by operators, linear transformations                 of a space that is usually infinite-dimensional. This replacement               is what mathematical physicists call quantization. The general                  idea is that the operators behave almost like the functions from                which they arise, except for correction terms which turn out to                 contain important information. In this line of endeavor, physical               insight informs mathematics as often as the reverse.
{'FirstName': 'Lewis', 'LastName': 'Coburn', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Lewis A Coburn', 'EmailAddress': 'lcoburn@acsu.buffalo.edu', 'NSF_ID': '000328279', 'StartDate': '06/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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