## Linear Operators: Spectral theory |

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2 9 Hilbert space H and let E

2 9 Hilbert space H and let E

**denote**its resolution of the identity . Then there erists a sequence { x } C H such that y = $ ( x ; ) , where H Li - 1 H H ( « ; ) sp { f ( T ) x ; \ ; e C ( o ( T ) ) } , and a decreasing sequence { en } ...Page 1126

i = of the closed set C ; we shall

i = of the closed set C ; we shall

**denote**this subspace of L , [ 0 , 1 ] by the symbol s2 ( C ) . Since each projection in the spectral resolution of T and hence each continuous function of T is a strong limit of linear combinations of ...Page 1486

In the next few paragraphs t

In the next few paragraphs t

**denotes**a formally self adjoint formal differential operator of order n , defined on the interval R = { - 00 < t < +0 . Let t have the form T n dii T = , ) 9 dt j = 0 and suppose that all the coefficients a ...### 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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk 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