## Linear Operators: Spectral theory |

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Page 1383

With boundary conditions A, the

from the equation sin V2 = 0. Consequently, in Case A, the

numbers of the form (nar)”, n > 1; in Case C, the numbers {(n+})*}”, n > 0.

With boundary conditions A, the

**eigenvalues**are consequently to be determinedfrom the equation sin V2 = 0. Consequently, in Case A, the

**eigenvalues**A are thenumbers of the form (nar)”, n > 1; in Case C, the numbers {(n+})*}”, n > 0.

Page 1497

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

the

entirely of

infinity.

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

the

**eigenvalue**H-1; in the latter case, to the ... and T, whose spectra consistentirely of

**eigenvalues**which, by Lemma 29 and Corollary 24, approach plusinfinity.

Page 1615

Reference: Rosenfeld, N. S., The

Operators, Comm. Pure Appl. Math. 18, 395–405 (1960). He proves the following

theorem. THEOREM. Let q(t) < 0 be twice continuously differentiable, lim, so q(t) ...

Reference: Rosenfeld, N. S., The

**Eigenvalues**of a Class of Singular DifferentialOperators, Comm. Pure Appl. Math. 18, 395–405 (1960). He proves the following

theorem. THEOREM. Let q(t) < 0 be twice continuously differentiable, lim, so q(t) ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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