## Linear Operators: Spectral theory |

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Page 1217

Two ordered representations U and Ở of H relative to T and I

measures j and û , and multiplicity sets { en } and { ēn } will be called equivalent if

u = û and ulendēn ) = ( ) = ülendên ) for n = 1 , 2 , . . . . 16 THEOREM .

Two ordered representations U and Ở of H relative to T and I

**respectively**, withmeasures j and û , and multiplicity sets { en } and { ēn } will be called equivalent if

u = û and ulendēn ) = ( ) = ülendên ) for n = 1 , 2 , . . . . 16 THEOREM .

Page 1302

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

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**. The statement of the present corollary is then evident .Page 1736

24 ( as generalized to D . , , ( C ) ) that we can extend fe and gę to elements fe

and ĝe in H % ) ( C ) and H 2 - 2p + 1 ) ( C ) ,

Klettese ...

24 ( as generalized to D . , , ( C ) ) that we can extend fe and gę to elements fe

and ĝe in H % ) ( C ) and H 2 - 2p + 1 ) ( C ) ,

**respectively**, having carriers ,**respectively**, equal to the carriers of fs and gs , and that we then have ( 00 +Klettese ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive 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 differential equations 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 Proc projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero