## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1662

Let I be an open

Let I be an open

**subset**of C , and let F be in D. ( 1 ) . Then the closed set Cp in I , which is the complement 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**...Page 1663

for each open

for each open

**subset**I. of I whose closure is compact and contained in I. 35 DEFINITION . Let I be an open**subset**of C and let k be a positive integer . ( i ) The set of all F in D ( 1 ) for which ( F ( 0 ) | | F | ( -4 ) sup < 0 PEC ...Page 1696

By Lemma 14 there is a sequence { Fm } of elements of D ( I ) , each of which has a carrier which is a compact

By Lemma 14 there is a sequence { Fm } of elements of D ( I ) , each of which has a carrier which is a compact

**subset**Cm of I , and such that F , → F as m + 00. Hence , we can evidently suppose without loss of generality that the ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator 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 shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero