## Linear Operators: Spectral theory |

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Page 978

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 that ...

**Closure**Theorems It was As in the preceding section the letter R will stand for anondiscrete locally compact Abelian group and integration will always be

performed with respect to a Haar measure on the group . observed in Corollary

5.2 that ...

Page 1226

This fact leads us to make the following definition . 7 DEFINITION . The minimal

closed symmetric extension of a symmetric operator T with dense domain is

called its

restriction of ...

This fact leads us to make the following definition . 7 DEFINITION . 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 therestriction of ...

Page 1687

tinuous in the

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. Lemma 3.13 ( iv ) )

.

tinuous in the

**closure**of D. This will evidently imply the truth of the presenttheorem . 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. Lemma 3.13 ( iv ) )

.

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