## Linear Operators: Spectral theory |

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Page 1226

Part ( a ) follows immediately from

immediately from part ( a ) and

) that any symmetric operator with dense domain has a unique minimal closed

symmetric ...

Part ( a ) follows immediately from

**Lemma**5 ( b ) , and part ( b ) followsimmediately from part ( a ) and

**Lemma**5 ( c ) . Q.E.D. It follows from**Lemma**6 ( b) that any symmetric operator with dense domain has a unique minimal closed

symmetric ...

Page 1698

Using

by

) ( V ) , so that in case ( a ) we have shown that foqilis the limit in the norm of H ( P

) ...

Using

**Lemma**2.1 , let y be a function in CO ( V ) with y ( x ) = 1 for x in K. Then ,by

**Lemmas**3.22 and 3.10 , fooi ? = y ( fooi ? ) = limm - cWhm in the norm of H ( P) ( V ) , so that in case ( a ) we have shown that foqilis the limit in the norm of H ( P

) ...

Page 1733

Q.E.D.

neighborhood of the boundary of a domain with smooth boundary . This is carried

out in the next two

Q.E.D.

**Lemma**18 enables us to use the method of proof of Theorem 2 in theneighborhood of the boundary of a domain with smooth boundary . This is carried

out in the next two

**lemmas**. 19**LEMMA**. Let o be an elliptic formal partial ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 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