## Linear Operators: Spectral theory |

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Page 1236

Every closed

( T * ) determined by a

, . . . , k . Conversely , every such restriction T , of T * is a closed

Every closed

**symmetric**extension of T is the restriction of T * to the subspace of D( T * ) determined by a

**symmetric**family of boundary conditions , Bi ( x ) = 0 , i = 1, . . . , k . Conversely , every such restriction T , of T * is a closed

**symmetric**...Page 1238

Let T be a

, . . . , A , be a complete set of boundary values for T , and let 21 . j = 1 & isA ; Ā ,

be the bilinear form of Lemma 23 . A set of boundary conditions IP is Az ( x ) = 0 ...

Let T be a

**symmetric**operator with finite deficiency indices whose sum is p . Let A, . . . , A , be a complete set of boundary values for T , and let 21 . j = 1 & isA ; Ā ,

be the bilinear form of Lemma 23 . A set of boundary conditions IP is Az ( x ) = 0 ...

Page 1272

123 ] and Ahiezer and Glazman ( 1 ; Secs . 78 – 80 ] . Maximal

operators . If T is a

zero .

123 ] and Ahiezer and Glazman ( 1 ; Secs . 78 – 80 ] . Maximal

**symmetric**operators . If T is a

**symmetric**operator with dense domain , then it has proper**symmetric**extensions provided both of its deficiency indices are different fromzero .

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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