## Schwartz distributionsDept. of Pure Mathematics, School of General Studies; Dept. of Mathematics, Institute of Advanced Studies, Australian National University, 1969 - Mathematics - 95 pages |

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### Contents

Preliminaries | 1 |

The definition of distributions | 8 |

Derivatives and primitives | 18 |

Copyright | |

5 other sections not shown

### Common terms and phrases

absolutely integrable bounded support constant distribution continuous functions convolution of distributions convolution of functions Corollary corresponding defined differentiable functions distribution derivative distribution of bounded distributions of slow elementary solution equation equivalence classes example f and g fact finite number finite order follows Fourier coefficients Fourier series Fourier transforms functions f functions of bounded functions of slow given Hanna Neumann hence hypoelliptic implies infinitely interval a,b lim S*a locally integrable functions notation Note null set open interval containing periodic distribution periodic functions polynomial function primitives Proof properties prove Pure Mathematics remark Riemann Integral Schwartz's distributions slow growth space of distributions subspace support is contained tends to zero test functions Theorem trigonometric series vector space Weyl's Lemma