PARTICLE REPRESENTATIONS FOR FINITE GAP OPERATORS (BAKER-AKHIEZER).

Persistent Link:
http://hdl.handle.net/10150/184658
Title:
PARTICLE REPRESENTATIONS FOR FINITE GAP OPERATORS (BAKER-AKHIEZER).
Author:
SCHILLING, RANDOLPH JAMES.
Issue Date:
1982
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
It 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.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Matrices.; Hill determinant.; Harmonic analysis -- Mathematical models.; Neumann problem.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Flaschka, H.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titlePARTICLE REPRESENTATIONS FOR FINITE GAP OPERATORS (BAKER-AKHIEZER).en_US
dc.creatorSCHILLING, RANDOLPH JAMES.en_US
dc.contributor.authorSCHILLING, RANDOLPH JAMES.en_US
dc.date.issued1982en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.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.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMatrices.en_US
dc.subjectHill determinant.en_US
dc.subjectHarmonic analysis -- Mathematical models.en_US
dc.subjectNeumann problem.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorFlaschka, H.en_US
dc.identifier.proquest8227368en_US
dc.identifier.oclc682961897en_US
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