## Linear Operators, Part 2 |

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Page 890

2x } of T and otherwise let E ( 8 ) be the sum of all the projections E ( 2x ) for

which Ried , then the function E is a ... but in this situation it is necessary to define

the integral appearing in ( vi ) and to define the algebra of scalar

which ...

2x } of T and otherwise let E ( 8 ) be the sum of all the projections E ( 2x ) for

which Ried , then the function E is a ... but in this situation it is necessary to define

the integral appearing in ( vi ) and to define the algebra of scalar

**functions f**towhich ...

Page 986

that f is invariant under translations . This shows that I 2 L and completes the

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

Linear combinations of the translates of a

) if and ...

that f is invariant under translations . This shows that I 2 L 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 Ly ( R ) are dense in Ly ( R) if and ...

Page 1075

14 Show that there exists continuous functions in L ( -0 , too ) L ( -00 , +00 ) such

that the limit in Exercise 12 fails to exist for x = 0 . 15 Show that there exists a

) e ...

14 Show that there exists continuous functions in L ( -0 , too ) L ( -00 , +00 ) such

that the limit in Exercise 12 fails to exist for x = 0 . 15 Show that there exists a

**function f**in Lil - 00 , +00 ) for which the family of functions a 1 p + A ti ( x ) La F ( t) e ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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