## Linear Operators: Spectral theory |

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Page 1215

... ( ds ) exists in the mean square sense and equals ( UD ) . ( 2 ) , proving ( c ) . Q

. E . D . Using the notation of the

Lemma 9 , in a ( 2 ) W . ( : , 2 ) ua ( da ) = E ( [ - n , n ] ) F ( T ) a → F ( T ) a = U ; F =

fa .

... ( ds ) exists in the mean square sense and equals ( UD ) . ( 2 ) , proving ( c ) . Q

. E . D . Using the notation of the

**preceding**proof we let F = ( Uf ) , so that , byLemma 9 , in a ( 2 ) W . ( : , 2 ) ua ( da ) = E ( [ - n , n ] ) F ( T ) a → F ( T ) a = U ; F =

fa .

Page 1480

3 and Theorem 6 . 5 . By Lemma 51 there are an infinite number of points in o ( T

) below 20 . Thus it follows from Corollary 24 ( c ) and Lemma 21 that llin + 10 .

That Yn is unique and has exactly n - 1 zeros is proved just as in the

3 and Theorem 6 . 5 . By Lemma 51 there are an infinite number of points in o ( T

) below 20 . Thus it follows from Corollary 24 ( c ) and Lemma 21 that llin + 10 .

That Yn is unique and has exactly n - 1 zeros is proved just as in the

**preceding**...Page 1771

0 - 1 ( 2 ) u ( 1 , 2 ) = 0 , t > 0 , 62 , and such that lim ( u ( t , : ) - 1 ( : ) ] = 0 . t - 0

Proof . Statement ( i ) follows from the

Statement ( ii ) follows from statement ( ii ) of the

0 - 1 ( 2 ) u ( 1 , 2 ) = 0 , t > 0 , 62 , and such that lim ( u ( t , : ) - 1 ( : ) ] = 0 . t - 0

Proof . Statement ( i ) follows from the

**preceding**theorem and Theorem 6 . 23 .Statement ( ii ) follows from statement ( ii ) of the

**preceding**theorem , since a ...### What people are saying - Write a review

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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