## Linear Operators: Spectral theory |

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Page 1142

The validity of the

from its validity in the range 2 P S 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 < 2 now follows at oncefrom its validity in the range 2 P S 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 1679

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

show that ( 4 ) G ( S , ¥ ( • ) pl . – y ) f ( y ) dy ) = S , G ( ( • 9 ( • – 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 ( S , ¥ ( • ) pl . – y ) f ( y ) dy ) = S , G ( ( • 9 ( • – y ) ) / ( y ) dy ,

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

compact ...

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 ( E ) ( and

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

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 ( E ) ( and

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

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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