## Linear Operators: Spectral theory |

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Page 1176

Let p , q , kn be as in the preceding lemma , and , for each N , let X y be the

transformation in L , ( la ) which maps the

Fourier transform fn ( 5 ) into the

transform ...

Let p , q , kn be as in the preceding lemma , and , for each N , let X y be the

transformation in L , ( la ) which maps the

**vector**whose nth component has theFourier transform fn ( 5 ) into the

**vector**whose nth component has the Fouriertransform ...

Page 1178

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

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 , X ...

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

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 , X ...

Page 1751

s differentiable m -

C ) will denote the subspaces of Ĉ ~ ( C ) consisting of all functions which are

multiply periodic of period 27 and of all functions which vanish outside a compact

...

s differentiable m -

**vector**valued functions defined in C. Similarly , © ( C ) and © (C ) will denote the subspaces of Ĉ ~ ( C ) consisting of all functions which are

multiply periodic of period 27 and of all functions which vanish outside a compact

...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### Common terms and phrases

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