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Preface to the Russian Edition Chapter
Normed Spaces Comparability and Compatibility of Norms
Countably Normed Spaces
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according analogous Applying assertion assume Axiom belongs bounded set called Chapter compact complete condition conjugate consider consists constant constructed contains continuous linear functional converges converges to zero convolution corresponding countably normed space defined definition derivatives domain element entire function equals equation equivalent estimate evidently example exists expression fact finite fixed formula Fourier transform functional f fundamental function fundamental space Furthermore given Hence holds infinitely differentiable functions integral introduce Lemma Let us consider Let us show limit linear topological space means Mp(x multiplication neighborhood of zero nontrivial obtain operator order of growth particular possible Proof properties proved qu(x replaced respect result satisfying the inequalities Section sequence space K(a space Ø spaces of type strong strongly sufficient tends to zero theorem theory topology translation turn uniformly union valid values vanish verify virtue Volume weak weakly