## Linear Operators, Part 2 |

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Page 1079

Show that if 11 , ... , in are

Show that if 11 , ... , in are

**eigenvalues**of A ( each**eigenvalue**2 being repeated a number of times equal to the dimension of the range of E ( 1 ; A ) ) , then the**eigenvalues**of Am ) are die din ... him iz , ig , ... , im being an ...Page 1383

With boundary conditions A , the

With boundary conditions A , the

**eigenvalues**are consequently to be determined from the equation sin vă = 0 . Consequently , in Case A , the**eigenvalues**1 are the numbers of the form ( na ) , n 2 1 ; in Case C , the numbers { ( n + 1 ) ...Page 1615

Reference : Rosenfeld , N. S. , The

Reference : Rosenfeld , N. S. , The

**Eigenvalues**of a Class of Singular Differential Operators , Comm . Pure Appl . Math . 13 , 395–405 ( 1960 ) . He proves the following theorem . THEOREM . Let g ( t ) < o be twice continuously ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero