## Linear Operators: Spectral theory |

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Page 1215

Q.E.D. Using the notation of the

Q.E.D. Using the notation of the

**preceding**proof we let F ( Uf ) , so that , by Lemma 9 , 11 > S " . ( Uf ) , ( 2 ) Wall . , 294a ( da ) = E ( [ –n , n ] ) F ( T ) a a ) ma [ - , ] ) → F ( T ) a = U.F = fa . N Thus the integral 8.Page 1480

By Lemma 51 there are an infinite number of points in o ( T ) below no . Thus it follows from Corollary 24 ( c ) and Lemma 21 that un → 10 . That Pn is unique and has exactly n - 1 zeros is proved just as in the

By Lemma 51 there are an infinite number of points in o ( T ) below no . Thus it follows from Corollary 24 ( c ) and Lemma 21 that un → 10 . That Pn is unique and has exactly n - 1 zeros is proved just as in the

**preceding**theorem .Page 1771

Statement ( i ) follows from the

Statement ( i ) follows from the

**preceding**theorem and Theorem 6.23 . Statement ( ii ) follows from statement ( ii ) of the**preceding**theorem , since a function satisfying ...### 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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity 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