## Linear Operators: Spectral theory |

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Page 1656

Let k be an integer and let F be a distribution in I. (i) If each point p in I has a

compact and each point p in I has a

then Fe ...

Let k be an integer and let F be a distribution in I. (i) If each point p in I has a

**neighborhood**U, contained in I such that FIU, e A*(U.), then Fe A*(I). (ii) If I iscompact and each point p in I has a

**neighborhood**U, such that FIU, I e Ho(U,I),then Fe ...

Page 1678

Let to be a second function in Co(I) such that j(r) = 1 for a in a

. Then pop—op vanishes in a

...

Let to be a second function in Co(I) such that j(r) = 1 for a in a

**neighborhood**of K1. Then pop—op vanishes in a

**neighborhood**of K n C(F), and vanishes in a**neighborhood**of C(F)—K since p vanishes in the complement of K. Hence pp-op...

Page 1733

Q.E.D. Lemma 18 enables us to use the method of proof of Theorem 2 in the

out in the next two lemmas. 19 LEMMA. Leto be an elliptic formal partial

differential ...

Q.E.D. Lemma 18 enables us to use the method of proof of Theorem 2 in the

**neighborhood**of the boundary of a domain with smooth boundary. This is carriedout in the next two lemmas. 19 LEMMA. Leto be an elliptic formal partial

differential ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero