Mathematical Sciences: Subnormal Operators and Related      Topics
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Operator theory is a central discipline in Modern Analysis.             Its origins lie in the study of mathematical physics and partial                differential equations in the early twentieth century.  Thus, it                was seen that numerous physical problems in the theory of                       equilibria, vibration, quantum theory, etc. could be studied                    productively via the integral equations that model the phenomena.               So it has been, that from the fertile minds of Hilbert, von                     Neumann, and other giants that the subject of operator theory has               grown to a central position in such investigations, and in core                 mathematics as well.  At the heart of this methodology is the                   deep investigation of the spectrum of an operator and the                       concommitant study of its invariant subspaces.  For the so-called               self-adjoint operators, this theory is now a standard technique                 throughout analysis, and the spectral theorem provides the                      necessary building blocks for all such operators.  Although not                 quite as complete, spectral theory is significantly well                        understood for an extensive generalization of the self-adjoint                  case; viz., the "normal" operators.  The current frontier,                      therefore, in the study of this structure theory rests in the                   non-normal theory.                                                                      Professors Conway has long been a leader in the study of                subnormal operators, a broad class of operators that arise in                   applications, and for which there is enough residual normal                     information to attempt a deeper understanding of their inherent                 structure.  Recent results, suchas the fact that subnormal                      operators are reflexive and have invariant subspaces, have given                an added impetus to the study of their spectral properties.                     Since many explicit operators that arise in complex function                    theory, differential geometry, and approximation theory  are                    subnormal, there is a broad range of developing interaction.                    Professor Conway will study subnormal operators that arise                      naturally in actions on Hardy spaces, thereby exploring the                     interaction with function theory.  He will also investigate the                 internal structure theory of subnormal operators, with particular               consideration of unitary equivalence, bundle shifts, and the                    relationship with general operator theory.
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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