Mathematical Sciences: Nonlinear Harmonic Analysis
{'Code': '03040103', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez'}
This project is for mathematical research on singular                      integral operators and related matters.  These operators                        transform functions which may be quite chaotic in their behavior                into functions which are very smooth.  The study of their                       continuity properties, that is, how small changes in the input                  function show up in the transformed function, is basic to much of               mathematical analysis.  Such investigations are part of the                     research which Professor Semmes will undertake.                                      Surfaces in space give rise to singular integral operators;                these will be studied with the aim of relating continuity                       properties of the operators to geometric properties of the                      surfaces.  A collateral group of problems to be pursued has to                  with the complex method of interpolation of Banach spaces from                  the viewpoint of differential geometry and differential                         equations.
{'FirstName': 'Stephen', 'LastName': 'Semmes', 'EmailAddress': 'semmes@rice.edu', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'William Marsh Rice University', 'CityName': 'Houston', 'ZipCode': '770051827', 'PhoneNumber': '7133484820', 'StreetAddress': '6100 MAIN ST', 'CountryName': 'United States', 'StateName': 'Texas', 'StateCode': 'TX'}
{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8804281.xml'}