## Linear Operators: Spectral theory |

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Page 984

The set of functions f in Ly ( R ) for which s

is dense in Ly ( R ) . Proof . It follows from Lemma 3 . 6 that the set of all functions

in L2 ( R , B , u ) which

The set of functions f in Ly ( R ) for which s

**vanishes**in a neighborhood of infinityis dense in Ly ( R ) . Proof . It follows from Lemma 3 . 6 that the set of all functions

in L2 ( R , B , u ) which

**vanish**outside of compact sets is dense in this space ...Page 993

It remains to be proved that the number ay is independent of the open set V . If f is

in Lj ( R ) L2 ( R ) , f

open subset V , of V , then the above proof shows that ( 0f ) ( m ) = Qy for every ...

It remains to be proved that the number ay is independent of the open set V . If f is

in Lj ( R ) L2 ( R ) , f

**vanishes**on the complement of V , and f ( m ) = 1 for m in anopen subset V , of V , then the above proof shows that ( 0f ) ( m ) = Qy for every ...

Page 997

Since of is in L ( R ) , L ( R ) whenever f is , it follows that Ø maps each function in

L ( R ) , L ( R ) into a continuous function on R which

THEOREM . Let y be a bounded measurable function on R . Then a point m , in Ř

is in ...

Since of is in L ( R ) , L ( R ) whenever f is , it follows that Ø maps each function in

L ( R ) , L ( R ) into a continuous function on R which

**vanishes**at Poo . 23THEOREM . Let y be a bounded measurable function on R . Then a point m , in Ř

is in ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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