## Linear Operators: Spectral theory |

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Page 1272

If T is a symmetric operator with dense domain , then it has proper symmetric

extensions provided both of its deficiency

maximal symmetric operator is one which has no proper symmetric extensions ;

hence , a ...

If T is a symmetric operator with dense domain , then it has proper symmetric

extensions provided both of its deficiency

**indices**are different from zero . Amaximal symmetric operator is one which has no proper symmetric extensions ;

hence , a ...

Page 1398

Therefore T , has a proper symmetric extension T2 , and the proof is complete . Q

. E . D . 8 COROLLARY . Let t be a formally self adjoint formal differential operator

defined on an interval 1 . If the minimum of the deficiency

Therefore T , has a proper symmetric extension T2 , and the proof is complete . Q

. E . D . 8 COROLLARY . Let t be a formally self adjoint formal differential operator

defined on an interval 1 . If the minimum of the deficiency

**indices**of To ( t ) is k ...Page 1610

( 16 ) Suppose that [ a , b ) = [ 0 , 00 ) , that the deficiency

and that there exists a sequence { In } of square - integrable functions such that in

vanishes in the interval [ 0 , n ] , \ tal = 1 , and l ( at ) in SK . Then the interval [ 2 - K

...

( 16 ) Suppose that [ a , b ) = [ 0 , 00 ) , that the deficiency

**indices**of t are equaland that there exists a sequence { In } of square - integrable functions such that in

vanishes in the interval [ 0 , n ] , \ tal = 1 , and l ( at ) in SK . Then the interval [ 2 - K

...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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