## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 63

Page 1099

... finite matrix may be approximated arbitrarily closely by non -

it is sufficient to consider the case in which T is non -

/ 2 is also non -

... finite matrix may be approximated arbitrarily closely by non -

**singular**matrices ,it is sufficient to consider the case in which T is non -

**singular**. Then A = ( TT * ) 1/ 2 is also non -

**singular**and if U = A - 17 , UU * = A - 1 A2A - 1 = 1 , then U is ...Page 1584

The contemporary research of Hellinger [ 1 ] , E . Schmidt [ 1 , 2 ] and Hilbert [ 1 ]

on integral equations naturally led to an interest in a similar approach to

differential operators whose coefficients are

endpoints of ...

The contemporary research of Hellinger [ 1 ] , E . Schmidt [ 1 , 2 ] and Hilbert [ 1 ]

on integral equations naturally led to an interest in a similar approach to

differential operators whose coefficients are

**singular**at one or both of theendpoints of ...

Page 1919

7 ( 136 )

258 ) , IV . 5 . 3 ( 259 ) , IV . 6 . 2 – 3 ( 262 – 264 ) , IV . 8 . 16 ( 296 ) definitions , (

160 – 162 ) , IV . 2 . 15 - 17 ( 240 ) , IV . 6 . 1 ( 261 ) remarks on , ( 389 - 390 )

study ...

7 ( 136 )

**singular**, III . 4 . 12 ( 131 ) spaces of , as conjugate spaces , IV . 5 . 1 (258 ) , IV . 5 . 3 ( 259 ) , IV . 6 . 2 – 3 ( 262 – 264 ) , IV . 8 . 16 ( 296 ) definitions , (

160 – 162 ) , IV . 2 . 15 - 17 ( 240 ) , IV . 6 . 1 ( 261 ) remarks on , ( 389 - 390 )

study ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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