## The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier AnalysisThe main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration. |

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### Contents

1 | |

Definition and Basic Properties of Distributions | 33 |

Differentiation and Multiplication by Functions | 54 |

Convolution | 87 |

Distributions in Product Spaces | 126 |

Composition with Smooth Maps | 133 |

The Fourier Transformation | 158 |

### Other editions - View all

The analysis of linear partial differential operators, Volume 1 Lars Hörmander No preview available - 1983 |

### Common terms and phrases

analytic function assume boundary value bounded Cauchy problem choose closed Cº(IR Cº(X compact set compact subset compact support completes the proof conic neighborhood continuous function converges convex cone convolution coordinates Corollary CŞ(X defined definition denote derivatives differential operator distribution entire analytic function equal estimate exists extension fact finite follows from Theorem Fourier transform fundamental solution gives Hence homogeneous of degree Hörmander hyperfunctions implies integral Lemma limit Malgrange preparation theorem manifold Math notation Note obtain open set partial differential equations partition of unity polynomial preceding exercise proof of Theorem pseudo-differential operators Pure Appl real analytic replaced restriction right-hand side satisfies Section sequence shows sing suppu singularities space supp test functions theory unique vanishes variables vector wave front set WF(u zero