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

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Page 1151

To prove the normality of R we shall use this

disjoint closed sets in R. We select an open set G , in R such that Fin K , Įg , Gin

F , = 0 , and then choose an open set H , such that F , K , CH , Ā , n ( F , UG ...

To prove the normality of R we shall use this

**remark**inductively . Let F , and F , bedisjoint closed sets in R. We select an open set G , in R such that Fin K , Įg , Gin

F , = 0 , and then choose an open set H , such that F , K , CH , Ā , n ( F , UG ...

Page 1381

By the

f ( 1 ) form a complete set of boundary values for t , and the most general self

adjoint extension To of T. ( t ) is defined by a boundary condition f ( 0 ) = eiŪ ] ( 1 )

.

By the

**remark**following Definition 2.29 , the two linear functionals f + f ( 0 ) and | +f ( 1 ) form a complete set of boundary values for t , and the most general self

adjoint extension To of T. ( t ) is defined by a boundary condition f ( 0 ) = eiŪ ] ( 1 )

.

Page 1472

On the other hand , if two linearly independent solutions of to = lo satisfy the

boundary condition B , it follows that all solutions of to = ho satisfy B. By the

and a < c ...

On the other hand , if two linearly independent solutions of to = lo satisfy the

boundary condition B , it follows that all solutions of to = ho satisfy B. By the

**remark**( a ) made above , it then follows that for any two solutions f , g of τσ = ho ,and a < c ...

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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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