Generalized Functions: Spaces of fundamental and generalized functionsAcademic Press, 1964 - Functions |
Contents
Preface to the Russian Edition | 1 |
Countably Normed Spaces | 15 |
Continuous Linear Functionals and the Conjugate Space | 32 |
Copyright | |
17 other sections not shown
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Common terms and phrases
A₁ analogous analytic function axiom of countability B₁ belongs bounded set bounded support C₁ Chapter complete countably normed condition conjugate space constant continuous function continuous linear functional converges to zero converges uniformly convolution countably normed space defined definition derivatives domain G element entire analytic function entire function exp(a finite formula Fourier transform function f(x functional ƒ functions of bounded fundamental function fundamental space Hence infinitely differentiable functions initial topology integral Lemma Let us consider Let us show limit linear operator linear topological space M₂(x Mp(x multiplication neighborhood of zero nontrivial obtain order of growth perfect space polynomial Proof proved satisfying the inequalities SB.B Section space K(a space K{M space Ø space SB spaces of type strongly bounded sufficient system of norms tends to zero theorem uniform convergence x₁ y₁