## Linear Operators, Volume 2 |

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Page 978

**Closure**Theorems It was As in the preceding section the letter R will stand for a nondiscrete locally compact Abelian group and integration will always be performed with respect to a Haar measure on the group . observed in Corollary 5.2 ...Page 1226

The minimal closed symmetric extension of a symmetric operator T with dense domain is called its

The minimal closed symmetric extension of a symmetric operator T with dense domain is called its

**closure**, and written T. 8 LEMMA . ( a ) The**closure**T of T is the restriction of T * to the**closure**of D ( T ) in the Hilbert space D ( T ...Page 1687

tinuous in the

tinuous in the

**closure**of D. This will evidently imply the truth of the present theorem . First suppose that U is disjoint from the boundary of D. Then h ; F is a distribution whose carrier is a compact set contained in U ( cf.### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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additive adjoint operator 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 derivatives 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 neighborhood norm obtained partial positive preceding present problem 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 vanishes vector zero