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

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Page 1217

Two ordered representations U and of H relative to T and †

measures u and ù , and multiplicity sets { en } and { en } will be called equivalent

if u ħ and u ( e , děn ) = 0 = ülendēm ) for n = 1 , 2 , .... 16 THEOREM . A

separable ...

Two ordered representations U and of H relative to T and †

**respectively**, withmeasures u and ù , and multiplicity sets { en } and { en } will be called equivalent

if u ħ and u ( e , děn ) = 0 = ülendēm ) for n = 1 , 2 , .... 16 THEOREM . A

separable ...

Page 1302

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

Jacob T. Schwartz. Corollary 23 and from Theorems 19 and 20 that d ' and d '

exceed by n the number of independent boundary values at a and at b

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

Jacob T. Schwartz. Corollary 23 and from Theorems 19 and 20 that d ' and d '

exceed by n the number of independent boundary values at a and at b

**respectively**.Page 1736

... fe and ge in HA ) ( C ) and H. - 20 + 1 ) ( C ) ,

fe + tele = ĝe Moreover , by Lemma 3.24 ( as generalized to Dr , ( C ) ) , fe is in H .

.

... fe and ge in HA ) ( C ) and H. - 20 + 1 ) ( C ) ,

**respectively**, having carriers ,**respectively**, equal to the carriers of tę and ge , and that we then have ( 0 , + K )fe + tele = ĝe Moreover , by Lemma 3.24 ( as generalized to Dr , ( C ) ) , fe is in H .

.

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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

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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