## Linear Operators: Spectral theory |

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Page 1217

If u ( ek ) > 0 for all k , the representation is said to have infinite multiplicity . Two

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

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

if u ħ ...

If u ( ek ) > 0 for all k , the representation is said to have infinite multiplicity . Two

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

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

if u ħ ...

Page 1302

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

statement of the present corollary is then evident . Q . E . D . 26 COROLLARY . (

Kodaira ) ...

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**. Thestatement of the present corollary is then evident . Q . E . D . 26 COROLLARY . (

Kodaira ) ...

Page 1548

extensions of S and Ŝ

defined for the self adjoint operators T and Î as in Exercise D2 . Show that in ( T )

2 an ( † ) , n 2 1 . Dil Let T , be a self adjoint operator in Hilbert space H , , and let

T ...

extensions of S and Ŝ

**respectively**, and let 2 ( T ) and 2n ( Î ) be the numbersdefined for the self adjoint operators T and Î as in Exercise D2 . Show that in ( T )

2 an ( † ) , n 2 1 . Dil Let T , be a self adjoint operator in Hilbert space H , , and let

T ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present 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 unit vanishes vector zero