## Linear Operators: Spectral theory |

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Page 1079

Show that if 21 , . . . , dn are

a number of times equal to the dimension of the range of E ( 2 ; A ) ) , then the

Show that if 21 , . . . , dn are

**eigenvalues**of A ( each**eigenvalue**à being repeateda number of times equal to the dimension of the range of E ( 2 ; A ) ) , then the

**eigenvalues**of A ( m ) are hin die . . . him in , iz , . . . , im being an arbitrary ...Page 1383

With boundary conditions A , the

from the equation sin vã = 0 . Consequently , in Case A , the

numbers of the form ( na ) ? , n 2 1 ; in Case C , the numbers { ( n + ) a } ? , n 2 0 ...

With boundary conditions A , the

**eigenvalues**are consequently to be determinedfrom the equation sin vã = 0 . Consequently , in Case A , the

**eigenvalues**are thenumbers of the form ( na ) ? , n 2 1 ; in Case C , the numbers { ( n + ) a } ? , n 2 0 ...

Page 1497

In the former case the matrix B ( 2 ) necessarily has an eigenvector belonging to

the

of

In the former case the matrix B ( 2 ) necessarily has an eigenvector belonging to

the

**eigenvalue**+ 1 ; in the latter case , to the**eigenvalue**– 1 . Thus , in ... entirelyof

**eigenvalues**which , by Lemma 29 and Corollary 24 , approach plus infinity .### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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