## Linear Operators: Spectral theory |

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Page 1079

Show that if 12 , ... , in are

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

of ...

Show that if 12 , ... , in are

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

**eigenvalues**of A ( m ) are hindi , ... him ij , ig , ... , im being an arbitrary sequenceof ...

Page 1383

With boundary conditions A , the

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

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

...

With boundary conditions A , the

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

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

...

Page 1615

Reference : Rosenfeld , N. S. , The

Operators , Comm . Pure Appl . Math . 13 , 395–405 ( 1960 ) . He proves the

following theorem . THEOREM . Let alt ) < o be twice continuously differentiable ...

Reference : Rosenfeld , N. S. , The

**Eigenvalues**of a Class of Singular DifferentialOperators , Comm . Pure Appl . Math . 13 , 395–405 ( 1960 ) . He proves the

following theorem . THEOREM . Let alt ) < o be twice continuously differentiable ...

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