Linear algebra and differential geometry on abstract Hilbert space

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dc.creatorKryukov, Alexey A.
dc.date2007-04-24
dc.date.accessioned2026-07-07T07:58:01Z
dc.date.available2026-07-07T07:58:01Z
dc.descriptionIsomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R^n, Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of local coordinates on Hilbert manifolds. Images of charts on manifolds in the formalism are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations then describe families of functional equations on various spaces of functions. The formalism itself and its applications in linear algebra, differential equations and differential geometry are analyzed.
dc.description37 pages, 3 figures, see http://www.uwc.edu/dept/math/faculty/kryukov/ for additional applications
dc.identifierhttps://arxiv.org/abs/0704.3225
dc.identifierhttp://arxiv.org/abs/0704.3225
dc.identifierInt. J. Math & Math. Sci. 14, 2241 (2005)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127855
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.subject46C05; 46F12; 46T05; 81Q70
dc.titleLinear algebra and differential geometry on abstract Hilbert space
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