## Linear Operators: Spectral theory |

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Page 1245

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

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

lei81 = 1 . By analogy with the

self ...

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

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

lei81 = 1 . By analogy with the

**fact**that r = ( ac ) , we shall first seek to obtain theself ...

Page 1348

are in

the solutions of to = lo . However , in the range à < 0 , 25 is imaginary , and an

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

are in

**fact**entire in 2 . In the range a > 0 they form a perfectly suitable basis forthe solutions of to = lo . However , in the range à < 0 , 25 is imaginary , and an

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

Page 1386

This

interest since it serves to emphasize the

orthonormal eigenfunctions of a differential operator can be obtained directly

from the ...

This

**fact**has already been noted ; but the present derivation is of particularinterest since it serves to emphasize the

**fact**that the normalization factors for theorthonormal eigenfunctions of a differential operator can be obtained directly

from the ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

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