Mathematical Sciences: Partial Differential Equations, GroupRepresentations and Number Theory
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
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Ehrenpreis                                                                      8805909                                                                              This project will encompass three areas of mathematical                    analysis, each of which represents a continuation of earlier                    research.  The first concerns the extensions of solutions of                    partial differential equations from domains which have the                      shape of convex wedges to surrounding domains when the wedges                   share common boundary elements.  In its general form the goal                   is to determine the relations among the Cauchy data on the                      boundary which imly the extendability of solutions.  Solutions                  have been obtained for constant coefficient equations in low                    dimentions.                                                                          Work will also be done on problems of scattering theory.                   A recent concept of nonabelian mechanics in which the                           poisson bracket of space variables makes the space and momentum                 into seperate Lie algebras (rather than vanishing), when                        suitably paired.  This approach leads to a new notion of                        completely integrable systems which can be applied to                           scattering problems on nonabelian groups.  Work planned seeks                   to develop this research in higher dimensions.                                       Efforts will also continue on the question of determining                  when a left-invariant operater on a Lie group can  be                           surjective on the infinitely differentiable functions.  This                    work derives from earlier research on the so-called Lewy                        operater - a partial differential equation with no solutions.                   Initial results using the Husenberg group suggest that a                        general framework for deciding on the surjectivity of                           differential operators and hence the conditions under which one                 can expect solutions of the corresponding inhomogeneous                         equations.
{'FirstName': 'Leon', 'LastName': 'Ehrenpreis', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Leon Ehrenpreis', 'EmailAddress': 'leon@math.temple.edu', 'NSF_ID': '000164682', 'StartDate': '07/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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