## Linear Operators: Spectral theory |

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Page 966

For some choice of f the integral on the right of [*] is not zero and since, by

Lemma 1 (d), the integral on the left of [*] is

agrees almost everywhere with a

measure ...

For some choice of f the integral on the right of [*] is not zero and since, by

Lemma 1 (d), the integral on the left of [*] is

**continuous**, we conclude that h,agrees almost everywhere with a

**continuous**function. By redefining h, on a set ofmeasure ...

Page 968

PRoof. Verification that the neighborhoods N(h, K, e) are a base for a topology

will be left to the reader. If hi e N(h, K, e) and he e N(ho, K, e) then hi ha e N(hho,

K*, e) so that multiplication is

PRoof. Verification that the neighborhoods N(h, K, e) are a base for a topology

will be left to the reader. If hi e N(h, K, e) and he e N(ho, K, e) then hi ha e N(hho,

K*, e) so that multiplication is

**continuous**. If h, e N(h, K, e) then hı" e N(h-", K, e), ...Page 1903

(See also Absolutely

.15 definition, IV.2.14 (240) remarks concerning, (373-386) study of, IV.6

characterizations of C-space, (396– 397) on a compact space, I.5.8 (18), I.5.10 (

18) ...

(See also Absolutely

**continuous**functions) as a B-space, additional properties, IV.15 definition, IV.2.14 (240) remarks concerning, (373-386) study of, IV.6

characterizations of C-space, (396– 397) on a compact space, I.5.8 (18), I.5.10 (

18) ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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### Common terms and phrases

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