## Linear Operators: Spectral theory |

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Page 1347

This procedure has the

This procedure has the

**evident**advantage that it makes 0 ; ( :, 1 ) an entire function of the complex variable 2 ; but it has drawbacks which , though less**evident**, are nevertheless decisive . Suppose , for example , that we study the ...Page 1661

The analogs of Lemma 3 and Definition 4 are now

The analogs of Lemma 3 and Definition 4 are now

**evident**, and instead of stating them in the new context we shall simply refer to " Lemma 3 or Definition 4 as generalized to D ( 1 ) ” wherever necessary 31 TT DEFINITION .Page 1662

However , an

However , an

**evident**consequence of Lemma 12 , as generalized to D. ( I ) , which will be of importance to us in subsequent discussions , is stated in the following lemma . 33 LEMMA . Let I be an open subset of the interior of C ...### 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 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 Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero