## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1675

This completes the proof of the direct part of ( i ) of the

the converse , let F be in H ) ( C ) and let â Ê be in H ( C ) . Let us agree to

consider that each q in C ( C ) is extended by periodicity to a multiply periodic

function ...

This completes the proof of the direct part of ( i ) of the

**present**lemma . To provethe converse , let F be in H ) ( C ) and let â Ê be in H ( C ) . Let us agree to

consider that each q in C ( C ) is extended by periodicity to a multiply periodic

function ...

Page 1679

Using ( 1 ) and ( 3 ) , we see that to establish the

show that ( 4 ) G ( 5,46 * p * – y ) t ( y ) dy ) = 5,6 ( y ( • ) { • —y ) ) / ( y ) dy , where

G = YF . Let K , be a compact subset of I containing in its interior a second

compact ...

Using ( 1 ) and ( 3 ) , we see that to establish the

**present**lemma it suffices toshow that ( 4 ) G ( 5,46 * p * – y ) t ( y ) dy ) = 5,6 ( y ( • ) { • —y ) ) / ( y ) dy , where

G = YF . Let K , be a compact subset of I containing in its interior a second

compact ...

Page 1692

Since { 2,01m } is bounded in L2 ( C ) for each J with Jl Sp - 1 and for each j such

that i si sn , it is clear that the

special case , p = 1. However , this case p = 1 is the special case k = 1 , p ...

Since { 2,01m } is bounded in L2 ( C ) for each J with Jl Sp - 1 and for each j such

that i si sn , it is clear that the

**present**lemma will follow immediately from its ownspecial case , p = 1. However , this case p = 1 is the special case k = 1 , p ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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