## Linear Operators: Spectral theory |

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Page 1142

The validity of the

its validity in the range 2 Sp oo and from Lemma 9 . 14 . Q . E . D . In what follows

, we will use the symbols p and n to denote the continuous extension to the ...

The validity of the

**present**theorem in the range 1 < p S2 now follows at once fromits validity in the range 2 Sp oo and from Lemma 9 . 14 . Q . E . D . In what follows

, we will use the symbols p and n to denote the continuous extension to the ...

Page 1684

Hence , it is quite sufficient to prove the

. By Corollary 2 again , each derivative g of order 1 of F belongs to Lp ( Em ) ( and

has compact carrier ) , for every p ' satisfying the inequality ( i ) 1 1 ( k - 1 ) p ...

Hence , it is quite sufficient to prove the

**present**lemma for the special case m = 0. By Corollary 2 again , each derivative g of order 1 of F belongs to Lp ( Em ) ( and

has compact carrier ) , for every p ' satisfying the inequality ( i ) 1 1 ( k - 1 ) p ...

Page 1692

Since we have already seen that lim | f ( x ) - ( ) d = 0 m , m , - JK , for each j , it

follows that lim m ( x ) - Ím , ( x ) / " dx = 0 , m , m , * JI proving the

Q . E . D . 9 COROLLARY . The conclusions of Corollary 6 and Lemma 8 remain ...

Since we have already seen that lim | f ( x ) - ( ) d = 0 m , m , - JK , for each j , it

follows that lim m ( x ) - Ím , ( x ) / " dx = 0 , m , m , * JI proving the

**present**lemma .Q . E . D . 9 COROLLARY . The conclusions of Corollary 6 and Lemma 8 remain ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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