## Linear Operators: Spectral theory |

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Page 1383

With boundary conditions A and C, the unique solution of tso = Ao satisfying the

boundary condition raq = Mo is sin Våt. With boundary conditions A, the

With boundary conditions A and C, the unique solution of tso = Ao satisfying the

boundary condition raq = Mo is sin Våt. With boundary conditions A, the

**eigenvalues**are consequently to be determined from the equation sin V2 = 0.Page 1497

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

the

discrete

the ...

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

the

**eigenvalue**+1; in the latter case, ... By Theorem 64, we now see that thediscrete

**eigenvalues**of those two problems are the only possible end points inthe ...

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

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero