## Linear Operators: Spectral theory |

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Page 1142

The validity of the

from its validity in the range 2 Sp Soo 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 s 2 now follows at oncefrom its validity in the range 2 Sp Soo 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 , ¥ ( * ) p ( • — y ) f ( y ) dy ) = S , G ( y ( • ) q ( • — y ) ) f ( y ) dy ,

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

...

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

**present**lemma it suffices toshow that ( 4 ) G ( S , ¥ ( * ) p ( • — y ) f ( y ) dy ) = S , G ( y ( • ) q ( • — y ) ) f ( y ) dy ,

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

...

Page 1756

On the other hand , it follows from ( * * ) that VP = VP + 1 , so that , putting V = V1 ,

we have V in Ĉ ° ( En + 1 ) , and the

consequence of ( ii ) . The remainder of the

that ( ii ) is ...

On the other hand , it follows from ( * * ) that VP = VP + 1 , so that , putting V = V1 ,

we have V in Ĉ ° ( En + 1 ) , and the

**present**theorem is shown to be aconsequence of ( ii ) . The remainder of the

**present**proof is devoted to showingthat ( ii ) is ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 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 |

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