## Linear Operators: Spectral theory |

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Page 993

Then it

Then it

**follows**from what has just been demonstrated that av , = Oyuv , = dy , i.e. , ay is independent of v . Q.E.D. 0 1 16 THEOREM . If the bounded measurable function q has its spectral set consisting of the single point m then ...Page 996

Sat ( x ) g ( x ) dx Since f * q is continuous by Lemma 3.1 ( d ) it

Sat ( x ) g ( x ) dx Since f * q is continuous by Lemma 3.1 ( d ) it

**follows**from the above equation that f * 9 +0 . From Lemma 12 ( b ) it is seen that olf * ) Cole ) and from Lemma 12 ( c ) and the equation if = tf it**follows**that olf ...Page 1708

Since se is in Hm ) , it

Since se is in Hm ) , it

**follows**that there exists some F in Hm + p ) such that ( Tito ) F = že . However , since feq is in Hm + p - 1 ) , and since by ( 5 ) , ( t + oc ) fe9 = ge , it**follows**that teq = F is in 16m + p ) ( C ) so that ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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