## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1218

If the

and thus the class ... set o containing e and a closed set 8 contained in e with u (

0-8 ) < E. Clearly the

If the

**restrictions**flo , g | 8 are continuous then so is the**restriction**( af + Bg ) o n dand thus the class ... set o containing e and a closed set 8 contained in e with u (

0-8 ) < E. Clearly the

**restriction**of Xe to the complement of 0-8 is continuous .Page 1239

Conversely , let T , be a self adjoint extension of T. Then by Lemma 26 , T , is the

linearly independent boundary conditions B : ( x ) = 0 , i = 1 , ... , k , and we have ...

Conversely , let T , be a self adjoint extension of T. Then by Lemma 26 , T , is the

**restriction**of T * to a subspace W of D ( T * ) determined by a symmetric family oflinearly independent boundary conditions B : ( x ) = 0 , i = 1 , ... , k , and we have ...

Page 1471

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self

adjoint

70 , B ( f ) = B.G. ( 1 ) + B2G , ( t ) = 0 , Bi + B 0 , B1 , B2 real , if ı has boundary ...

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self

adjoint

**restriction**T of Ti ( t ) is of the form B ( 1 ) = a_G7 ( 1 ) +02 G2 ( / ) = 0 , aita70 , B ( f ) = B.G. ( 1 ) + B2G , ( t ) = 0 , Bi + B 0 , B1 , B2 real , if ı has boundary ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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