## Linear Operators: Spectral theory |

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Page 1236

A set of boundary conditions B , ( x ) = 0 , i = 1 , ... , k , is said to be

equations B , ( x ) = B ; ( y ) = 0 , i = 1 , ... , k , imply the equation { x , y } 0 . 26

LEMMA . Let T be an operator with finite deficiency indices . Every closed

A set of boundary conditions B , ( x ) = 0 , i = 1 , ... , k , is said to be

**symmetric**if theequations B , ( x ) = B ; ( y ) = 0 , i = 1 , ... , k , imply the equation { x , y } 0 . 26

LEMMA . Let T be an operator with finite deficiency indices . Every closed

**symmetric**...Page 1238

Let T be a

A1 , ... , A , be a complete set of boundary values for T , and let X2,3–10i , A ; Ā ,

be the bilinear form of Lemma 23 . A set of boundary conditions X - Bi ; A ; ( x ) = 0

...

Let T be a

**symmetric**operator with finite deficiency indices whose sum is p . LetA1 , ... , A , be a complete set of boundary values for T , and let X2,3–10i , A ; Ā ,

be the bilinear form of Lemma 23 . A set of boundary conditions X - Bi ; A ; ( x ) = 0

...

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Maximal

then it has proper

are different from zero . A maximal

proper ...

Maximal

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

**symmetric**extensions provided both of its deficiency indicesare different from zero . A maximal

**symmetric**operator is one which has noproper ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero