## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1051

Self Adjoint Operators in Hilbert Space. Spectral theory. Part II Nelson Dunford,

Jacob T. Schwartz. Plenh ( x ) dx PSen f ( x ) dx . Proof . Statement ( i ) is

from Definition 1. Statements ( ii ) and ( iii ) are

Definition ...

Self Adjoint Operators in Hilbert Space. Spectral theory. Part II Nelson Dunford,

Jacob T. Schwartz. Plenh ( x ) dx PSen f ( x ) dx . Proof . Statement ( i ) is

**evident**from Definition 1. Statements ( ii ) and ( iii ) are

**evident**consequences ofDefinition ...

Page 1173

PROOF . We first consider the special case p = q . The space L , ( Lp ) may in an

the inequality to be proved reduces to ( 41 ) SoS . 2 ( x - y ) \ x - y " fly , s ) dy dxds

...

PROOF . We first consider the special case p = q . The space L , ( Lp ) may in an

**evident**manner be identified with the Lo - space on the product set E " XS andthe inequality to be proved reduces to ( 41 ) SoS . 2 ( x - y ) \ x - y " fly , s ) dy dxds

...

Page 1661

The analogs of Lemma 3 and Definition 4 are now

them in the new context we shall simply refer to “ Lemma 3 or Definition 4 as

generalized to D , ( 1 ) ” wherever necessary . 31 DEFINITION . Suppose that I is

an ...

The analogs of Lemma 3 and Definition 4 are now

**evident**, and instead of statingthem in the new context we shall simply refer to “ Lemma 3 or Definition 4 as

generalized to D , ( 1 ) ” wherever necessary . 31 DEFINITION . Suppose that I is

an ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

### Common terms and phrases

additive 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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero