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

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Page 1297

Q.E.D. We now turn to a discussion of the specific form assumed in the present case by the abstract “

Q.E.D. We now turn to a discussion of the specific form assumed in the present case by the abstract “

**boundary values**" introduced in the last chapter . We shall see that the discussion leads us to a number of results about deficiency ...Page 1307

**boundary values**C1 , C2 , D1 , D , where C ,, C , are**boundary values**at a and D2 , D , are**boundary values**at b , such that ... Let A be any**boundary value**for T. Since t is real , D ( T ( T ) ) is closed under the formation of complex ...Page 1471

01 , 2 , real , if t has no

01 , 2 , real , if t has no

**boundary values**at b ; while if t has**boundary values**at b , we may find two real**boundary values**D ,, , for T , at b , such that ( tzt , g ) – ( 1 , 728 ) = D ( 1 ) D2 ( g ) – Dg ( 1 ) D , ( g ) –F : 1 , g ) ...### 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