Mathematical Sciences: Functional Analysis and Functional   Theory
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
This project is mathematical research in certain areas of                  function theory.  Functions in the plane satisfying rather simple               partial differential equations, for instance analytic and                       harmonic functions, turn out to have properties which make them                 both useful and fascinating.  A fundamental property exhibited by               such functions is that their values on a simple closed curve                    completely determine their values at points inside.  One can                    study harmonic and analytic functions so to speak concretely, or                one can take a more abstract approach by forming Banach spaces or               algebras of appropriate kinds of functions and applying the                     methods of functional analysis.  The investigators specialize in                attacking concrete problems with abstract methods.                                  More specifically, the topics to be investigated include                    uniform algebras, algebras of bounded analytic functions, the                   corona problem in the plane, estimates for harmonic measure, and                the spectral theory of certain types of Schroedinger operators.
[{'FirstName': 'Theodore', 'LastName': 'Gamelin', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Theodore W Gamelin', 'EmailAddress': 'twg@math.ucla.edu', 'NSF_ID': '000383595', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'John', 'LastName': 'Garnett', 'PI_MID_INIT': 'B', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John B Garnett', 'EmailAddress': 'jbg@math.ucla.edu', 'NSF_ID': '000433036', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'University of California-Los Angeles', 'CityName': 'LOS ANGELES', 'ZipCode': '900244200', 'PhoneNumber': '3107940102', 'StreetAddress': '10889 WILSHIRE BLVD STE 700', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '36', 'CONGRESS_DISTRICT_ORG': 'CA36', 'ORG_UEI_NUM': 'RN64EPNH8JC6', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA, LOS ANGELES', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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