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

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Page 951

When integration is with respect to Haar measure , as is generally the case , we

write dx instead of a ( dr ) . ... ( b ) For f , geLy ( R ) the

integrable in y for almost all x and the convolution f * g

defined by ...

When integration is with respect to Haar measure , as is generally the case , we

write dx instead of a ( dr ) . ... ( b ) For f , geLy ( R ) the

**function f**( x , y ) g ( y ) isintegrable in y for almost all x and the convolution f * g

**of f**and g , which isdefined by ...

Page 986

that f is invariant under translations . This shows that I 21 and completes the proof

of the lemma . Q.E.D. 7 THEOREM . ( Wiener L , -closure theorem ) . Linear

combinations of the translates of a

only ...

that f is invariant under translations . This shows that I 21 and completes the proof

of the lemma . Q.E.D. 7 THEOREM . ( Wiener L , -closure theorem ) . Linear

combinations of the translates of a

**function f**in Li ( R ) are dense in L ( R ) if andonly ...

Page 1646

It is clear that if F corresponds to the

g in the sense of the above definition , then aF + BG corresponds to of + Bg . Thus

the linear space of functions integrable on each compact subset of I may be ...

It is clear that if F corresponds to the

**function f**and G corresponds to the functiong in the sense of the above definition , then aF + BG corresponds to of + Bg . Thus

the linear space of functions integrable on each compact subset of I may be ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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