## Linear Operators: Spectral theory |

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Page 1650

of I in which F vanishes , is called the carrier or support of F . 12 LEMMA . Let I be

...

**subsets**of I and let F be in D ( I ) . If F vanishes in each ... Let K be a compact**subset**of Ugla outside of which y vanishes . ... of the union of all the open**subsets**of I in which F vanishes , is called the carrier or support of F . 12 LEMMA . Let I be

...

Page 1660

Of course , if we deal only with

identifications are made and the phrases ... If I is an open

modified sense explained in the preceding paragraph , then CO ( 1 ) will denote

the ...

Of course , if we deal only with

**subsets**of the interior of the cube C in E " , noidentifications are made and the phrases ... If I is an open

**subset**of C , in themodified sense explained in the preceding paragraph , then CO ( 1 ) will denote

the ...

Page 1695

Lemma 13 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 13 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 { In } be a sequence of open**subsets**of I whose union is I...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix 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