## A Course in Distribution Theory and ApplicationsBased on a series of lectures given to post-graduate students, this largely self-contained book makes distribution theory attainable to not only mathematics students, but also to those studying physics and engineering. It defines distributions using convergence concepts. Topics covered include Schwartz distributions, distributional derivatives, distributions of compact support, certain boundary value problems, and topological vector space theory. |

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see inside the book

### Contents

Preface | 1 |

Convergence of Distributions | 20 |

Differentiation of Distributions | 28 |

Convolution of Distributions | 38 |

Tempered Distributions and Fourier Transforms | 57 |

Sobolev Spaces | 79 |

20 | 96 |

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and/e Applications assume balanced and absorbing bilinear boundary value problem bounded open subset Bp(r called Cauchy sequence compact set compact subset compact support continuous function continuous linear functional continuous linear map converges to zero convolution countable union space definition denote dense subspace diffeomorphism dual element Example exists a unique finite formula functions defined given Hence Hilbert space identity map If/e implies inner product inverse Fourier transform Lax-Milgram Theorem Lemma Let Q Let/be Let/e locally integrable function manifold metric minimizes the functional Moreover norm open set open subset pA(x pk(x pn(x positive constant Proo Proof Let properties Prove satisfies seminorm sesquilinear functional Sobolev Space space H subset of Q tempered distribution test functions topological vector space u e H weak solution x g(y