Topological Vector Spaces, Distributions and Kernels

Released on by François Treves
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  • Topological Vector Spaces, Distributions and Kernels Book Detail

  • Author : François Treves
  • Release Date : 2016-06-03
  • Publisher : Elsevier
  • Genre : Mathematics
  • Pages : 582
  • ISBN 13 : 1483223620
  • File Size : 16,16 MB
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Topological Vector Spaces, Distributions and Kernels by François Treves PDF Summary

Book Description: Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.

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