## Generalized Functions: Spaces of fundamental and generalized functions, by I. M. Gelʹfand and G. E. Shilov, translated by M. D. Friedman, A. Feinstein, C. P. PeltzerAcademic Press, 1968 - Theory of distributions (Functional analysis) |

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### Contents

Chapter | 1 |

Normed Spaces Comparability and Compatibility of Norms | 11 |

Continuous Linear Functionals and the Conjugate Space | 32 |

Copyright | |

22 other sections not shown

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### Common terms and phrases

analogous axiom of countability belongs borhood bounded set bounded support Cauchy Chapter compact support complete countably normed condition conjugate space constant contains continuous function continuous linear functional converges to zero converges uniformly converges weakly convolution countably normed space definition differentiable functions p(x element pv entire analytic function entire function exists exp(a finite formula Fourier operator Fourier transform functions of bounded fundamental space Furthermore given Hence infinitely differentiable functions initial topology integral Lemma Let us consider Let us show limit linear operator linear topological space Mp(x Mv(x neighborhood of zero nontrivial obtain order of growth perfect space polynomial Proof proved result satisfying the inequalities Section sequence of functions sequence pv(x space 0p space K(a space K{Mp space SB-B space SJ spaces of type strong topology strongly bounded sufficient system of norms tends to zero theorem uniform convergence virtue weak convergence Z{Mp