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

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Page 1472

0 To = least one such

independent

all

that for ...

0 To = least one such

**solution**must exist . On the other hand , if two linearlyindependent

**solutions**of to = lo satisfy the boundary condition B , it follows thatall

**solutions**of to = ho satisfy B. By the remark ( a ) made above , it then followsthat for ...

Page 1521

The

precisely one

cases arise . Case 1. B 2 1/2 . Here the deficiency indices of Ly are zero , so that

no ...

The

**solution**at ho = 1 - i is exactly similar . Thus , by Theorem XII.4.19 , L , - , hasprecisely one

**solution**belonging to L ( 2 , 0 ) for each non - real 1. Thus twocases arise . Case 1. B 2 1/2 . Here the deficiency indices of Ly are zero , so that

no ...

Page 1529

Then in this angle any

the factor exp ( 511 ) ; & – 1 ) is exponentially small ( as ( 21 → oo in the angle )

relative to any

Then in this angle any

**solution**of Lf = 0 whose asymptotic expansion begins withthe factor exp ( 511 ) ; & – 1 ) is exponentially small ( as ( 21 → oo in the angle )

relative to any

**solution**whose asymptotic expansion begins with the factor exp ...### What people are saying - Write a review

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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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### 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