## Linear Operators: Spectral theory |

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Page 1086

... 8 ; - 1 ) , n + 1 Zi , j > 1 ; determines a kernel satisfying ( i ) of Exercise 44 ,

which represents the operator Dm - dn - 11 of the preceding exercise .

the series D ( 8 , t ; 2 ) = 2 61 , D , ( s , t ) n = 2 ( n - 1 ) ! converges for all 2 , for u

Xu ...

... 8 ; - 1 ) , n + 1 Zi , j > 1 ; determines a kernel satisfying ( i ) of Exercise 44 ,

which represents the operator Dm - dn - 11 of the preceding exercise .

**Moreover**,the series D ( 8 , t ; 2 ) = 2 61 , D , ( s , t ) n = 2 ( n - 1 ) ! converges for all 2 , for u

Xu ...

Page 1298

functional on D ( T1 ) . A similar argument holds for B , . Thus B , and B , are

boundary values for t . If g ( t ) = 0 in a neighborhood of a , then tage D ( T . ) by

Definition 8 ...

**Moreover**, by the continuity of the map g + 118 , B , is a continuous linearfunctional on D ( T1 ) . A similar argument holds for B , . Thus B , and B , are

boundary values for t . If g ( t ) = 0 in a neighborhood of a , then tage D ( T . ) by

Definition 8 ...

Page 1480

Tassociated with Ilon , and an has precisely n - 1 zeros . Proof . Since oe ( t ) n ( -

00 , 20 ) is void , then every point in o ( T ) n ( - 00 , 20 ) is isolated by Corollary 6 .

**Moreover**, there is a unique ( up to constant multiple ) eigenfunction on ofTassociated with Ilon , and an has precisely n - 1 zeros . Proof . Since oe ( t ) n ( -

00 , 20 ) is void , then every point in o ( T ) n ( - 00 , 20 ) is isolated by Corollary 6 .

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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