Mathematical Sciences: First-Order Elliptic Systems in      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}
This project provides support for continuing work on                        boundary problems associated with families of first-order                       systems of overdetermined, elliptic differential equations. The                 corresponding differential operators originate in the                           generalized potential theory in harmonic analysis on both                       Euclidean and Riemannian symmetric spaces. Applications to                      Euclidean Hardy-space theory and to explicit realization of                     unitarizable exceptional representations of semi-simple Lie                     groups will be made.  Because of emphasis on group invariances,                 polynomial invariant theory will play an increasingly important                 role in these investigations.  Further work on the                              group-theoretic connections will also be carried out. The                       ellipticity of the systems ensures the completeness of the                      normed spaces in which the solutions can be found while the                     over-determinedness allows one to study just the harmonic real                  parts of the (complex) functions under consideration.
{'FirstName': 'John', 'LastName': 'Gilbert', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John C Gilbert', 'EmailAddress': 'jgilbert@scu.edu', 'NSF_ID': '000414113', 'StartDate': '02/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Texas at Austin', 'CityName': 'AUSTIN', 'ZipCode': '787121139', 'PhoneNumber': '5124716424', 'StreetAddress': '110 INNER CAMPUS DR', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Texas', 'StateCode': 'TX', 'CONGRESSDISTRICT': '25', 'CONGRESS_DISTRICT_ORG': 'TX25', 'ORG_UEI_NUM': 'V6AFQPN18437', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF TEXAS AT AUSTIN', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8812414.xml'}