Topological Vector Spaces, Distributions and Kernels

analytic functional 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 element equal equicontinuous equicontinuous subset equivalent Exercise finite dimensional formal power series Fourier transformation Fréchet space function f functions with compact Hausdorff space Hausdorff TVS hence Hilbert space identical implies integral intersection isometry Lemma Let us denote LF-space linear subspace locally convex Hausdorff locally convex space metrizable neighborhood of zero normed space nuclear obviously 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