## Linear Operators: Spectral theory |

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Page 995

Let h be in L ( R ) with himo ) = 1 and h vanishing on an open set

remainder of olf * ° ) . It follows from Lemma 12 that the set ( h * f * 9 )

most the single point m , and hence , from Theorem 16 and Lemma 3 . 1 ( d ) ,

that ...

Let h be in L ( R ) with himo ) = 1 and h vanishing on an open set

**containing**theremainder of olf * ° ) . It follows from Lemma 12 that the set ( h * f * 9 )

**contains**atmost the single point m , and hence , from Theorem 16 and Lemma 3 . 1 ( d ) ,

that ...

Page 996

Thus , by hypothesis , olf * 9 )

Lemma 19 . Q . E . D . The next result shows in a striking manner the relations

between the study of spectral synthesis and the original L , closure theorem of N .

Wiener .

Thus , by hypothesis , olf * 9 )

**contains**an isolated point which contradictsLemma 19 . Q . E . D . The next result shows in a striking manner the relations

between the study of spectral synthesis and the original L , closure theorem of N .

Wiener .

Page 1397

The method of proof is the following : it will be shown that if the theorem is false ,

then a proper symmetric extension T , of T can be constructed whose domain

properly

The method of proof is the following : it will be shown that if the theorem is false ,

then a proper symmetric extension T , of T can be constructed whose domain

properly

**contains**both D ( T ) and the null - space of T * . This readily yields a ...### What people are saying - Write a review

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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