Mathematical Sciences: Harmonic Analysis Related            To Weight Functions
{'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}
Work to be carried out on this project focuses on estimates                of differential operators and resulting uniqueness of solutions                 which can be shown to follow from such estimates.  Particular                   emphasis is to be placed on p-power integral conditions on the                  lower order coefficients of the operators.  Among the specific                  goals of the research is one of characterizing what has been                    termed the unique continuation properties of potentials in                      differential equalities.  These a priori measures determine when                a smooth function must vanish identically from very local                       vanishing of its derivatives.  Particular interest will be paid                 to the Laplace operator in which the potential is taken in the                  largest logical class, known as the Kato class.                                      Related work will also be carried out on questions of global               unique continuation in which vanishing of potentials below                      hyperplanes is to ensure that they vanish everywhere.  Results                  due to C. Fefferman for perturbations of the Laplacian confirm                  that unique continuation is possible for potentials with high                   index.  This research will seek to lower the condition to                       integrability for all powers greater than unity.  Efforts will                  also be made to apply any new result to the Dirac operator where                unique continuation is only verifiable in specific cases rather                 than function classes.                                                               They key to understanding inequalities needed in the work is               a restriction phenomenon which must be established.  Basically,                 these phenomena say that the quadratic norm of a Fourier                        transform confined to the surface of a sphere is dominated by the               weighted quadratic integral of its antecedent.  The weight is the               potential of the differential inequality.  This research will                   have fundamental implications in the field of elliptic partial                  differential equations.
{'FirstName': 'Sagun', 'LastName': 'Chanillo', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Sagun Chanillo', 'EmailAddress': 'chanillo@math.rutgers.edu', 'NSF_ID': '000206843', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Rutgers University New Brunswick', 'CityName': 'NEW BRUNSWICK', 'ZipCode': '089018559', 'PhoneNumber': '8489320150', 'StreetAddress': '3 RUTGERS PLZ', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New Jersey', 'StateCode': 'NJ', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'NJ12', 'ORG_UEI_NUM': 'M1LVPE5GLSD9', 'ORG_LGL_BUS_NAME': 'RUTGERS, THE STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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