Topological Vector Spaces, Distributions and KernelsCourier Corporation, 1 de jan. de 2006 - 565 páginas This text for upper-level undergraduates and graduate students focuses on key notions and results in functional analysis. Extending beyond the boundaries of Hilbert and Banach space theory, it explores aspects of analysis relevant to the solution of partial differential equations. The three-part treatment begins with topological vector spaces and spaces of functions, progressing to duality and spaces of distribution, and concluding with tensor products and kernels. The archetypes of linear partial differential equations (Laplace's, the wave, and the heat equations) and the traditional problems (Dirichlet's and Cauchy's) are this volume's main focus. Most of the basic classical results appear here. There are 390 exercises, several of which contain detailed information that will enable readers to reconstruct the proofs of some important results. |
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Topological Vector Spaces, Distributions and Kernels: Pure and ..., Volume 25 François Treves Visualização parcial - 2016 |
Topological Vector Spaces, Distributions and Kernels, Volume 25 Francois Treves Prévia não disponível - 1967 |
Termos e frases comuns
analytic function arbitrary Banach space basis of neighborhoods belongs bilinear bounded subset canonical mapping Cauchy filter Chapter closure coefficients compact set compact subset compact support complete complex numbers contained continuous functions continuous linear form continuous linear map continuous seminorm converges to zero convex balanced convex Hausdorff space COROLLARY countable Definition dense E₁ element equal equicontinuous equicontinuous subset Exercise F₁ finite dimensional Fourier transformation Fréchet space function f functions with compact Hausdorff space Hausdorff TVS hence Hilbert space identical implies injection integral intersection isometry Lemma Let us denote LF-space linear subspace locally convex Hausdorff locally convex space metrizable neighborhood of zero normed space nuclear one-to-one open set open subset polynomials Proposition Radon measure relatively compact resp seminorm sequence space of distributions suffices supp Suppose tensor product topological space topological vector space topology induced transpose