## Linear Operators, Part 2 |

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Page 996

From Lemma 12 ( b ) it is seen that olf * ) Colg ) and from Lemma 12 ( c ) and the equation of = Tf it follows that o ( f * 9 )

From Lemma 12 ( b ) it is seen that olf * ) Colg ) and from Lemma 12 ( c ) and the equation of = Tf it follows that o ( f * 9 )

**contains**no interior point of o ( P ) . Hence olf * 9 ) is a closed subset of the boundary of o ( Q ) .Page 1456

Suppose for definiteness that I

Suppose for definiteness that I

**contains**a neighborhood of the left end point a of I , so that , unless I = I ( in which case t = t , and t is evidently bounded below ) , I ,**contains**a neighborhood of the right end point b of 1 .Page 1700

Then ( i ) ifl , is a subdomain of I whose boundary

Then ( i ) ifl , is a subdomain of I whose boundary

**contains**E , then the conditions ( 0 , ( E ) ) " } ( x ) = 0 , αε Σ , 0 si 3 k - 1 , and ( 0 , ( E ) ) ' ( 1 . ) ( x ) = 0 , αε Σ . 0 Sisk - 1 , are equivalent ; ( ii ) if I , is 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 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