## Linear Operators: Spectral theory |

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Throughout the present section , we

Throughout the present section , we

**assume**for simplicity of statement that Hilbert space is separable . Subdiagonal representations of an operator are connected with the study of its invariant subspaces .Page 1429

**Assume**that ( a ) la ( t ) is bounded away from zero ; ( b ) az ( t ) is bounded , 0 < ksn . Then t has no boundary values at infinity . PROOF . Without loss of generality ,**assume**that a = 0. Let t ' be the formally self adjoint formal ...Page 1629

Qt ; the coefficients diq ... i ( t1 , ... , tn ) being

Qt ; the coefficients diq ... i ( t1 , ... , tn ) being

**assumed**to be defined for t = [ t1 , ... ... let us**assume**that D is all of Euclidean n - dimensional space , and that S is a hyperplane of n - 1 dimensions in D. Making a suitable ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero