## 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 R with compact

from what has just been demonstrated that zy, = ovuv, -zy, i.e., xy is independent

of V. Q.E.D. 16 THEoREM. If the bounded measurable function op has its ...

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

**closure**. Then it followsfrom what has just been demonstrated that zy, = ovuv, -zy, i.e., xy is independent

of V. Q.E.D. 16 THEoREM. If the bounded measurable function op has its ...

Page 1226

The minimal closed symmetric extension of a symmetric operator T with dense

domain is called its

restriction of To to the

T ...

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 To to the

**closure**of Q(T) in the Hilbert space Q(T*). (b) The operatorT ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity 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