## 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 . It was observed in

Corollary 5 .

**Closure**Theorems 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 . It was observed in

Corollary 5 .

Page 993

Now let V , be an arbitrary open subset of Ř with compact

from what has just been demonstrated that ay , = Qyuv , = Qy , i . e . , Qy is

independent of V . Q . E . D . 16 THEOREM . If the bounded measurable function

o has ...

Now let V , be an arbitrary open subset of Ř with compact

**closure**. Then it followsfrom what has just been demonstrated that ay , = Qyuv , = Qy , i . e . , Qy is

independent of V . Q . E . D . 16 THEOREM . If the bounded measurable function

o has ...

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 ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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