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

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Page 1151

To prove the normality of R we shall use this

To prove the normality of R we shall use this

**remark**inductively . Let F , and F , be disjoint closed sets in R. We select an open set G , in R such that Fin K , CG , Gin F , = 0 , and then choose an open set Hį such that F , OKC H.Page 1381

By the

By the

**remark**following Definition 2.29 , the two linear functionals | → | ( 0 ) and | → | ( 1 ) form a complete set of boundary values for t , and the most general self adjoint extension T , of To ( T ) is defined by a boundary ...Page 1472

We summarize the above

We summarize the above

**remarks**for future reference in the following lemma . ... By**remark**( b ) preceding Lemma 41 , the adjoint of T * of T is the restriction of T ( T ) defined by the boundary conditions B ( if t has boundary values ...### 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 |

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