Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

An infinite-dimensional Hamiltonian system on projective Hilbert space


Author: Anthony M. Bloch
Journal: Trans. Amer. Math. Soc. 302 (1987), 787-796
MSC: Primary 58F05; Secondary 58F07, 70H05, 81C99
MathSciNet review: 891647
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Abstract: We consider here the explicit integration of a Hamiltonian system on infinite-dimensional complex projective space. The Hamiltonian, which is the restriction of a linear functional to this projective space, arises in the problem of line fitting in complex Hilbert space (or, equivalently, the problem of functional approximation) or as the expectation value of a model quantum mechanical system. We formulate the system here as a Lax system with parameter, showing how this leads to an infinite set of conserved integrals associated with the problem and to an explicit formulation of the flow in action-angle form via an extension of some work of J. Moser. In addition, we find the algebraic curve naturally associated with the system.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0891647-5
Article copyright: © Copyright 1987 American Mathematical Society