## Abstract Methods in Partial Differential Equations |

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### Contents

FUNCTIONAL ANALYSIS AND DISTRIBUTIONS | 1 |

The Space | 7 |

Differentiation in 2 and Examples | 9 |

Copyright | |

28 other sections not shown

### Other editions - View all

Abstract Methods in Partial Differential Equations Robert W. Carroll,Mathematics Limited preview - 2012 |

### Common terms and phrases

algebraically and topologically analytic arbitrary assume Banach algebra bounded operator bounded sets Cauchy Cauchy problem commutes compact set Consequently consider continuous linear map continuous map convergence corollary d/dt definition demicontinuous denotes domain duality element elliptic equations equicontinuous equivalent example exercise exists fact finite finite-dimensional follows formula functions functor Further given hence Hilbert space homomorphism hypotheses implies integral isomorphism lemma manifolds maximal accretive means measurable monotone morphism norm obtain obvious open nbh open set particular polynomial problem Proof Let proof of theorem prove recall refer reflexive Banach space relatively compact remark resp satisfies self-adjoint semigroup seminorms sequence sesquilinear form Similarly solution spectral spectral sets strongly subspace suitable supp suppose theorem 5.1 theory topology uniformly unique variable vector bundles vector space weak topology weakly write