## 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 ...

scalar

**functions**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 ...

Page 1178

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

, of scalar - valued

which maps the vector - valued

It is plain from Plancherel ' s theorem that X 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 1645

If we let 4 be its closure , we find that D ( 1 ) contains nondifferentiable

... In order for such an answer to make sense , it is desirable that we should be

able to define 0 , 0 , for every

If we let 4 be its closure , we find that D ( 1 ) contains nondifferentiable

**functions**.... In order for such an answer to make sense , it is desirable that we should be

able to define 0 , 0 , for every

**function**, differentiable or not , and irrespective of ...### What people are saying - Write a review

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero