Mathematical Sciences: Analysis on Nilpotent Lie Groups
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The theory of Lie groups, named in honor of the Norwegian                  mathematician Sophus Lie, has been one of the major themes in                   twentieth century mathematics.  As the mathematical vehicle for                 exploiting the symmetries inherent in a system, Lie theory has                  had a profound impact upon mathematics itself and theoretical                   physics, especially quantum mechanics and elementary particle                   physics.                                                                             The research proposed by Professor Jenkins utilizes the                    representation theory of nilpotent Lie groups to study certain                  classes of differential operators.  These include Schrodinger                   operators, which are the operators that determine the dynamical                 laws in quantum mechanical systems.  Given a differential                       operator, one constructs an appropriate Lie group in which that                 operator is realized infinitesimally in the universal enveloping                algebra.  This construction leads to a convolution semigroup of                 probability measures having the differential operator as                        infinitesimal generator.  In this way, Professor Jenkins uses the               theory of these semigroups to study the spectrum and                            corresponding eigenfunction expansion of the given operator.
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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