## Linear Operators: Spectral theory |

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Page 1650

which p vanishes. ... in I of the largest open set in I in which F vanishes, i.e., which

is the complement in I of the union of all the open

, ...

**subsets**of I and let F be in D(I). ... Let K be a compact**subset**of U.I. outside ofwhich p vanishes. ... in I of the largest open set in I in which F vanishes, i.e., which

is the complement in I of the union of all the open

**subsets**of I in which F vanishes, ...

Page 1663

that FIo is in Ho (Io) for each open

contained in I. 35 DEFINITION. Let I be an open

positive integer. (i) The set of all F in D, (I) for which |Fit-o = sup |F(p)| veco.(1)

play will be ...

that FIo is in Ho (Io) for each open

**subset**I, of I whose closure is compact andcontained in I. 35 DEFINITION. Let I be an open

**subset**of C and let k be apositive integer. (i) The set of all F in D, (I) for which |Fit-o = sup |F(p)| veco.(1)

play will be ...

Page 1695

Lemma 18 and the following lemma taken together give considerable insight into

the nature of distributions in general. 15 LEMMA. Let F be a distribution in the

open

Lemma 18 and the following lemma taken together give considerable insight into

the nature of distributions in general. 15 LEMMA. Let F be a distribution in the

open

**subset**I of E”. Let {I,} be a sequence of open**subsets**of I whose union is I, ...### What people are saying - Write a review

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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