## Linear Operators: Spectral theory |

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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 , CG , Gin

F , = 0 , and then choose an open set Hį such that F , OKC H. , Ho ( FU 3 , ) = 6 .

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 , CG , Gin

F , = 0 , and then choose an open set Hį such that F , OKC H. , Ho ( FU 3 , ) = 6 .

Page 1381

By the

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

adjoint extension T , of To ( T ) is defined by a boundary condition f ( 0 ) = pi ...

By the

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

adjoint extension T , of To ( T ) is defined by a boundary condition f ( 0 ) = pi ...

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

a < c < b ...

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 ho , anda < c < b ...

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

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