## Linear Operators: Spectral theory |

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Page 1241

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. then ,

letting 2n = Xn - Yn , we have limn _ 02n = 0 and limm . n - > 2m 2n | + = 0 .

, given ε ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. then ,

letting 2n = Xn - Yn , we have limn _ 02n = 0 and limm . n - > 2m 2n | + = 0 .

**Consequently**there is a number M such that Izml + SM , m = 1 , 2 , . . . . Moreover, given ε ...

Page 1383

With boundary conditions A , the eigenvalues are

from the equation sin vā = 0 .

numbers of the form ( na ) , n 21 ; in Case C , the numbers { ( n + ) } ? , n 20 .

With boundary conditions A , the eigenvalues are

**consequently**to be determinedfrom the equation sin vā = 0 .

**Consequently**, in Case A , the eigenvalues , are thenumbers of the form ( na ) , n 21 ; in Case C , the numbers { ( n + ) } ? , n 20 .

Page 1387

with the kernel In > O , Il > 0 , 1 sin văs ( cos Vīt + i sin Vīt ) 1 sat , V sin Vāt ( cos

Vīsti sin Văs ) < s , va sin Văs ( cos vă - i sin Vāt ) - s < t , V sin Vāt ( cos Vās i sin ...

**Consequently**, by Theorem 3 . 16 , the resolvent R ( 2 ; T ) is an integral operatorwith the kernel In > O , Il > 0 , 1 sin văs ( cos Vīt + i sin Vīt ) 1 sat , V sin Vāt ( cos

Vīsti sin Văs ) < s , va sin Văs ( cos vă - i sin Vāt ) - s < t , V sin Vāt ( cos Vās i sin ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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