## 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 H , such that Fon K , CH4 , 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 , CG , Gin

F , = 0 , and then choose an open set H , such that Fon K , CH4 , 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 To ( t ) is defined by a boundary condition f ( 0 ) = ei ...

By the

**remark**following Definition 2 . 29 , the two linear functionals † — f ( 0 ) andf = | ( 1 ) form a complete set of boundary values for t , and the most general self

adjoint extension To of To ( t ) is defined by a boundary condition f ( 0 ) = ei ...

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 to = lo ,and a < c ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero