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Coordinate formalism on Hilbert manifolds

Kryukov, Alexey (2001) Coordinate formalism on Hilbert manifolds. [Preprint]

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      Abstract

      Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and infinite-dimensional manifolds deeply similar. In this context the infinite-dimensional counterparts of simple notions such as basis, dual basis, orthogonal basis, etc. are shown to be closely related to the choice of a model. It is also shown that in this formalism a single tensor equation on an infinite-dimensional manifold produces a family of functional equations on different spaces of functions.


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      Item Type: Preprint
      Keywords: Hilbert manifolds, infinite-dimensional manifolds
      Subjects: Specific Sciences > Mathematics
      Depositing User: Alexey Kryukov
      Date Deposited: 15 Oct 2001
      Last Modified: 07 Oct 2010 11:10
      Item ID: 440
      Public Domain: No
      URI: http://philsci-archive.pitt.edu/id/eprint/440

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