## Linear Operators: Spectral theory |

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Page 1051

Statement ( i ) is

consequences of Definition 1 and of the formulae Sen . ( x ) dx = Sen P ( Ux ) dx ,

SE ( ax ) dx = 101 - " fr9 ( x ) dx , which are valid for every Lebesgue integrable ...

Statement ( i ) is

**evident**from Definition 1 . Statements ( ii ) and ( iii ) are**evident**consequences of Definition 1 and of the formulae Sen . ( x ) dx = Sen P ( Ux ) dx ,

SE ( ax ) dx = 101 - " fr9 ( x ) dx , which are valid for every Lebesgue integrable ...

Page 1347

This procedure has the

function of the complex variable 2 ; but it has drawbacks which , though less

self adjoint ...

This procedure has the

**evident**advantage that it makes 0 ; ( ' , 2 ) an entirefunction of the complex variable 2 ; but it has drawbacks which , though less

**evident**, are nevertheless decisive . Suppose , for example , that we study theself adjoint ...

Page 1756

( B ) The uniqueness of the function V of the theorem is an

of statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the

existence of the function V ' to the proof of the following statement . ( ii ) For each r

...

( B ) The uniqueness of the function V of the theorem is an

**evident**consequenceof statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the

existence of the function V ' to the proof of the following statement . ( ii ) For each r

...

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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