Special Functions and Orthogonal Expansions with            Applications to Nonlinear Dynamics and Quantum Mechanics
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This project combines the efforts of two investigators                     working on problems involving orthogonal expansions, special                    functions and their applications.  The program concerns                         investigations into qualitative and quantitative features of                    orthogonal polynomials in several variables and polynomials                     orthogonal with respect to complex weight functions.  Work is                   also planned on the application of elliptic functions to study                  spectral properties of orthogonal polynomials arising from                      stochastic processes and perturbation theory.                                        Additional work will be done investigating algorithms                      which reduce the complexity of equations describing quantum                     mechanics.  In particular, the applicability of Pade                            approximants or their radial simplifications will be considered.                     Related work involves the distribution of roots of complex                 orthogonal polynomials and Pade approximants.  The latter may                   shed light on the poles of Pade approximants in understanding                   resonance phenomena in non-linear dynamics.                                          While some of this research represents continuations of                    earlier work, that relating to multivariate polynomials follows                 recent breakthroughs following a period of intense research by                  a number of mathematicians.  Only during the past year have                     multivariate analogues of classical one-variable results been                   attained.  These include multivariate integrals extending the                   well-known gamma and beta integrals.                                                 The complexity of this research will require advanced                      computational support for testing and experimentation.
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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