## Linear Operators: Spectral theory |

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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 ) = eiŽ ] ( 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 ) = eiŽ ] ( 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 ...

Page 1900

Almost periodic functions , definition , IV.2.25 ( 242 ) space of , additional

properties , IV.15 ( 379 ) definition , IV.2.25 ( 242 )

387 ) study of , IV.7 Almost uniform ( or u - uniform convergence ) definition , III .

6.1 ( 145 ) ...

Almost periodic functions , definition , IV.2.25 ( 242 ) space of , additional

properties , IV.15 ( 379 ) definition , IV.2.25 ( 242 )

**remarks**concerning , ( 386–387 ) study of , IV.7 Almost uniform ( or u - uniform convergence ) definition , III .

6.1 ( 145 ) ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### Common terms and phrases

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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero