## Linear Operators, Part 2 |

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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 Ty , 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 Ty , 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 1611

( 1 ) If the essential spectrum of 1 is not the entire real axis , the deficiency

of t are equal ( 6 . 6 ) . ( 2 ) In particular , the deficiency

bounded below . ( 3 ) If for some real or complex 2 all solutions of the equation ( 2

...

( 1 ) If the essential spectrum of 1 is not the entire real axis , the deficiency

**indices**of t are equal ( 6 . 6 ) . ( 2 ) In particular , the deficiency

**indices**are equal if t isbounded below . ( 3 ) If for some real or complex 2 all solutions of the equation ( 2

...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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