## Linear Operators: Spectral theory |

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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 “

see that the discussion leads us to a number of results about deficiency indices ...

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 shallsee that the discussion leads us to a number of results about deficiency indices ...

Page 1307

, D , are

conjugate of the

linear ...

**boundary values**C , C2 , D2 , D , where C7 , C , are**boundary values**at a and D2, D , are

**boundary values**at b , such that ( tf ... We may call it the complexconjugate of the

**boundary value**A . The**boundary value**A may be written as alinear ...

Page 1471

if t has no

two real

1 ) D2 ( g ) — D2 ( 1 ) D2 ( 8 ) – Fr ( 1 , g ) , f , geD ( T2 ( 72 ) ) . By Theorem 2 .

if t has no

**boundary values**at b ; while if t has**boundary values**at b , we may findtwo real

**boundary values**D1 , D , for T , at b , such that ( T2 , g ) ( 1 , 728 ) = D2 (1 ) D2 ( g ) — D2 ( 1 ) D2 ( 8 ) – Fr ( 1 , g ) , f , geD ( T2 ( 72 ) ) . By Theorem 2 .

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 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 algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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