Mathematical Sciences: Complex and Harmonic Analysis
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
The aims of this project concern fundamental questions                     arising in the mathematical theory of several complex variables.                Work to be done involves the relationship of function theory on                 domains of finite type to the geometry of the boundaries of the                 domains.  Other work will focus on problems of classical function               theory and Euclidean harmonic analysis.                                              One important effort, of a continuing nature, is that of                   extending to domains in three or more complex dimensions, recent                results on pseudoconvex domains of finite type.  At this time,                  they have only been extablished in two dimensions.  The results                 concern the construction of a nonisotropic metric which estimates               the two most important integral kernels, the Bergman and Szego                  kernels.   As a consequence, sharp regularity properties of the                 Bergman and Szego projections are obtained.  This result is one                 of the foremost discoveries in the field in many years.                         Describing the corresponding result in higher dimensions is a                   natural and challenging  goal.                                                       Work on harmonic analysis will concentrate on estimates for                Fourier transforms defined along closed hypersurfaces in                        Euclidean space.  When the mainifold bounds a convex region,                    estimates of the transform are known. This research will seek to                obtain decay estimates for the transform when the manifold is not               convex.  A second objective will be to ask the same questions for               manifolds with higher codimension.  Work of this nature derives                 from problems in number theory and partial differential                         equations.                                                                           Other investigations will be carried out on finding proper                 conditions for the existence of Cauchy-Riemann extensions from                  submanifolds of finite type and on analyzing Bergman projections                in weighted spaces of entire functions in several complex                       variables.
{'FirstName': 'Alexander', 'LastName': 'Nagel', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Alexander Nagel', 'EmailAddress': 'nagel@math.wisc.edu', 'NSF_ID': '000123215', 'StartDate': '05/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Wisconsin-Madison', 'CityName': 'MADISON', 'ZipCode': '537151218', 'PhoneNumber': '6082623822', 'StreetAddress': '21 North Park Street', 'StreetAddress2': 'Suite 6301', 'CountryName': 'United States', 'StateName': 'Wisconsin', 'StateCode': 'WI', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'WI02', 'ORG_DUNS_NUM': '161202122', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WISCONSIN SYSTEM', 'ORG_PRNT_DUNS_NUM': '041188822'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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