## Linear Operators: Spectral theory |

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Page 1650

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

open ...

**subsets**of I and let F be in D(I). If F vanishes in each set I ... Let K be a compact**subset**of U.I. outside of which p vanishes. Using Lemma 2.4, let ...**subsets**of I inwhich F vanishes, is called the carrier or support of F. 12 LEMMA. Let I be an

open ...

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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 ...

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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 |

868 | 885 |

Miscellaneous Applications | 937 |

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