PARTICLE REPRESENTATIONS FOR FINITE GAP OPERATORS (BAKER-AKHIEZER).
AuthorSCHILLING, RANDOLPH JAMES.
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PublisherThe University of Arizona.
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AbstractIt is known that finite gap potentials of Hill's equation y" + q(τ)y = Ey can be obtained as solutions of an integrable dynamical system: uncoupled harmonic oscillators constrained to move on the unit sphere in configuration space--The Neumann System. This Dissertation systematizes and generalizes this result. First, the theory of Baker-Akhiezer functions is placed on a solid mathematical foundation. Guided by the theory of Baker-Akhiezer functions and Riemann surfaces, trace formulas, particle systems, constraints, integrals and Lax pairs are systematically constructed for the particle system of the ℓ x ℓ matrix differential operator of order n.
Degree ProgramApplied Mathematics