Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F05, 58F07, 70H05, 81C99

Retrieve articles in all journals with MSC: 58F05, 58F07, 70H05, 81C99

Additional Information

PII: S 0002-9947(1987)0891647-5
Article copyright: © Copyright 1987 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia