Mathematical Sciences: Function Theory on Convex Domains
{'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 project is concerned with mathematical research on the                 function theory on domains in the space of several complex                      variables.  Fundamental ideas from complex analysis, partial                    differential equations, operator theory and integral                            representations are combined in these investigations.  One basic                goal - well understood in one variable but open in several                      variables - is the classification of domains into equivalence                   classes under holomorphic coordinate changes.  Considerable                     progress has been made recently in this area through research on                related problems of extending holomorphic maps to the boundary of               regions.  This was done by analysis of the Bergman projection                   operator.                                                                            This focused attention on projections of functions onto                    holomorphic function spaces such as the Bergman and the Szego                   projections.  Work will be done analyzing the regularity                        properties of these and related projections on convex domains.                       Corvex domains with real analytic boundary are of finite                   type so that well known methods of partial differential                         equations can be used to show that these projection operators                   preserve differentiability of functions in Sobolev spaces.  Work                will be done in expanding present methods and developing new                    tools to handle domains of infinite type.
{'FirstName': 'Harold', 'LastName': 'Boas', 'PI_MID_INIT': 'P', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Harold P Boas', 'EmailAddress': 'boas@math.tamu.edu', 'NSF_ID': '000317117', 'StartDate': '07/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Texas A&M Research Foundation', 'CityName': 'COLLEGE STATION', 'ZipCode': '778454375', 'PhoneNumber': '9798626777', 'StreetAddress': '400 HARVEY MITCHELL PKWY S STE 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Texas', 'StateCode': 'TX', 'CONGRESSDISTRICT': '10', 'CONGRESS_DISTRICT_ORG': 'TX10', 'ORG_UEI_NUM': 'EQH8NQ4AXFT7', 'ORG_LGL_BUS_NAME': 'TEXAS A & M RESEARCH FOUNDATION', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701038.xml'}