Mathematical Sciences: Presidential Young Investigator
{'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 Presidential Young Investigator Award will support                    mathematical research in the area of harmonic analysis related to               problems of oscillatory integrals and differentiation theory.                   Several important directions will be followed during the period                 of support.  Many of these have their roots in questions                        concerning partial differential operators and efforts to measure                bounds on their solutions.  These include bounds on the norm of                 spectral projections involving spherical harmonic expansions of                 functions on a sphere.  Other work involves problems of Fourier                 analysis related to curvature of manifolds.  This includes                      development of uniform Sobolev inequalities and corresponding                   restriction theorems.  Results along these lines will provide                   powerful global conclusions from local inequalities.  Work will                 continue on the question of sharp Riesz means on arbitrary                      compact manifolds, especially regarding the weak type end point                 results which are invariably the most difficult to achieve.                          Other work will focus on unique continuation of second order               partial differential operators, especially Schrodinger operators,               unique continuation of hyperbolic and parabolic differential                    operators and related eigenfunction expansions.  A new area of                  work will concern maximal estimates for Randon transforms or                    averages of functions over lower dimensional surfaces.                          Interestingly the most difficult questions in this context occur                in lower dimensions where there has been considerable activity                  lately.
{'FirstName': 'Christopher', 'LastName': 'Sogge', 'PI_MID_INIT': 'D', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Christopher D Sogge', 'EmailAddress': 'sogge@jhu.edu', 'NSF_ID': '000246850', 'StartDate': '10/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Chicago', 'CityName': 'CHICAGO', 'ZipCode': '606375418', 'PhoneNumber': '7737028669', 'StreetAddress': '5801 S ELLIS AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'IL01', 'ORG_UEI_NUM': 'ZUE9HKT2CLC9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CHICAGO', 'ORG_PRNT_UEI_NUM': 'ZUE9HKT2CLC9'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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