## 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 5.2 that ...

**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 5.2 that ...

Page 993

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

from what has just been demonstrated that av , = dyuv , Ayur , = Qy , i.e. , Qy is

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

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

**closure**. Then it followsfrom what has just been demonstrated that av , = dyuv , Ayur , = Qy , i.e. , Qy is

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

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

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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 neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero