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

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Page 1301

They are clearly linearly

They are clearly linearly

**independent**. If the assertion of the corollary were false , it would follow that t has a boundary value at a which is**independent**of the set A. , ... , An - 1 , and hence has at least n + 1**independent**...Page 1306

The following table gives the number of linearly

The following table gives the number of linearly

**independent**solutions of ( 1-2 ) 0 = 0 square integrable at a or b when I ( a ) +0 . There are four possibilities as shown by the discussion above . At a Number of linearly**independent**...Page 1311

The operator T = T ( T ) will be an operator obtained from t by the imposition of a set , which may be vacuous , of k linearly

The operator T = T ( T ) will be an operator obtained from t by the imposition of a set , which may be vacuous , of k linearly

**independent**boundary conditions B ; ( ) 0 , 1 , ... , k ; i.e. , T is the restriction of T ( T ) ( cf.### 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