## Linear Operators: Spectral theory |

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Page 891

scalar

chapter we shall only integrate bounded

discussion of the integral will be restricted to that case . Let be a field of subsets

of a set S ...

scalar

**function**with respect to the operator valued set**function**E. In the presentchapter we shall only integrate bounded

**functions**| and so the followingdiscussion of the integral will be restricted to that case . Let be a field of subsets

of a set S ...

Page 1178

It is plain from Plancherel's theorem that K is a bounded mapping of the space L ,

of scalar - valued

which maps the vector - valued

It is plain from Plancherel's theorem that K is a bounded mapping of the space L ,

of scalar - valued

**functions**into the space L2 ... Let M be the mapping in L , ( 12 )which maps the vector - valued

**function**whose nth component has the Fourier ...Page 1922

Total space of functionals , definition , V.3.1 ( 418 ) Total variation of a

.5.15 ( 140 ) of a set

set , I.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ( 515 ) , XI.6.8 ( 1016 ) of a matrix ...

Total space of functionals , definition , V.3.1 ( 418 ) Total variation of a

**function**, III.5.15 ( 140 ) of a set

**function**, III.1.4 ( 97 ) . ( See also Variation ) Totally orderedset , I.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ( 515 ) , XI.6.8 ( 1016 ) of a matrix ...

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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