## Linear Operators: Spectral theory |

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Page 1211

Under

Under

**Hypothesis**7 , there is , for each g in L2 ( S , E , v ) , a function W defined on the Cartesian product of S and the real number system R which is measurable with respect to the product of v and the measure u ( E ( - ) g , g ) ...Page 1215

With the notation and

With the notation and

**hypothesis**of the preceding theorem we have 1 ( s ) ES ( UD ) ( A ) We ( 3 , 2 ) ! a ( 2 ) , fe L ( S , E , v ) , the integrals existing in the mean square sense in L ( S , & , v ) and the series converging in the ...Page 1734

By

By

**hypothesis**, no point in V but the points pleon U , ) belong to the boundary of q ( In U1 ) , and no point in E , is interior to the closure of I. It follows that q ( IU , ) must consist of one or another of the hemispheres V + = { x ...### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

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 complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives 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 Nauk 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