## Linear Operators: Spectral theory |

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Page 945

In

function fin AP has a unique extension to a function fi in C ( S ) . This follows from

Corollary IV.6.19 and the observation that the periodic ( and hence the almost ...

In

**fact**, R may be embedded as a dense subset of S in such a manner that everyfunction fin AP has a unique extension to a function fi in C ( S ) . This follows from

Corollary IV.6.19 and the observation that the periodic ( and hence the almost ...

Page 1245

This result may be regarded as a far - reaching generalization of the

each complex number a has a unique representation a reio , where r 20 , and

leiol 1. By analogy with the

...

This result may be regarded as a far - reaching generalization of the

**fact**thateach complex number a has a unique representation a reio , where r 20 , and

leiol 1. By analogy with the

**fact**that r = ( ão ) , we shall first seek to obtain the self...

Page 1348

are in

solutions of to 2o . However , in the range a < 0,2t is imaginary , and an analytic

expression like cos att is hard to work with because of the apparent ambiguity in ...

are in

**fact**entire in 2. In the range a > 0 they form a perfectly suitable basis for thesolutions of to 2o . However , in the range a < 0,2t is imaginary , and an analytic

expression like cos att is hard to work with because of the apparent ambiguity in ...

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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