## Linear Operators: Spectral theory |

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Page 1178

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 ( 12 ) of square - integrable

valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 ...

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 ( 12 ) of square - integrable

**vector**-valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 ...

Page 1749

Let V . ( x ) be an m -

differentiable there . Then there exists a unique m -

) , defined and infinitely often differentiable in En + 1 , such that j = 1 ( a ) V ( x ; 8 )

...

Let V . ( x ) be an m -

**vector**valued function defined in En and infinitely oftendifferentiable there . Then there exists a unique m -

**vector**valued function V ( x ; s) , defined and infinitely often differentiable in En + 1 , such that j = 1 ( a ) V ( x ; 8 )

...

Page 1849

On the one - dimensional translation group and semi - group in certain function

spaces . Dissertation , University of Uppsala ( 1950 ) . Math . Rev . 12 , 108 (

1951 ) . Ogasawara , T . 1 . Compact metric Boolean algebras and

On the one - dimensional translation group and semi - group in certain function

spaces . Dissertation , University of Uppsala ( 1950 ) . Math . Rev . 12 , 108 (

1951 ) . Ogasawara , T . 1 . Compact metric Boolean algebras and

**vector**lattices .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present 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 unit vanishes vector zero