## Linear Operators, Part 2 |

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preceding remarks that the final conclusion of the lemma is equivalent to the

preceding remarks that the final conclusion of the lemma is equivalent to the

**statement**that det ( A ) ( A - 1x , y ) = \ y ||| A || " -1 ( n - 1 ) - ( n - 1 ) / 2 . Now , since W is unitary , det ( A ) = det ( W - 1 AW ) and ( A - 1x ...Page 1463

**Statement**( a ) is the special case T = Tg of the preceding theorem .**Statement**( b ) is an evident consequence of**statement**( a ) . Q.E.D. The theorem is illustrated by the pair of functions sin it and sin ut for u > ; the corollary by ...Page 1771

**Statement**( i ) follows from the preceding theorem and Theorem 6.23 .**Statement**( ii ) follows from**statement**( ii ) of the preceding theorem , since a function satisfying the hypotheses of the present**statement**( ii ) evidently ( cf.### 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