## Linear Operators: Spectral theory |

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Page 1079

Show that if 21 , . . . , hn are

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

sequence ...

Show that if 21 , . . . , hn 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 die dig . . him ij , ia , . . . , im being an arbitrarysequence ...

Page 1383

With boundary conditions A , the

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

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 1615

Reference : Rosenfeld , N . S . , The

Differential Operators , Comm . Pure Appl . Math . 13 , 395 - 405 ( 1960 ) . He

proves the following theorem . THEOREM . Let g ( t ) < o be twice continuously

differentiable ...

Reference : Rosenfeld , N . S . , The

**Eigenvalues**of a Class of SingularDifferential Operators , Comm . Pure Appl . Math . 13 , 395 - 405 ( 1960 ) . He

proves the following theorem . THEOREM . Let g ( t ) < o be twice continuously

differentiable ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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