## 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 1703

In the

partial differential operators to be defined below . A crucial theorem in the

development of the theory of Chapter XIII was Theorem XIII . 2 . 10 , which was

based on ...

In the

**present**section it will be seen that it can , at least for the class of ellipticpartial differential operators to be defined below . A crucial theorem in the

development of the theory of Chapter XIII was Theorem XIII . 2 . 10 , which was

based on ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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