## Linear Operators: Spectral theory |

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Results 1-3 of 68

Page 1472

least one such

independent

all

that for any ...

least one such

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

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

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

Page 1529

Then in this angle any

the factor exp ( 517 ) * - 1 ) is exponentially small ( as [ 2 ] → o in the angle )

relative to any

51 ) ...

Then in this angle any

**solution**of Lj = 0 whose asymptotic expansion begins withthe factor exp ( 517 ) * - 1 ) is exponentially small ( as [ 2 ] → o in the angle )

relative to any

**solution**whose asymptotic expansion begins with the factor exp (51 ) ...

Page 1556

What is the relationship between 0 ( t ) and the number of zeros of a

the above equation ? G14 Use the result of the preceding exercise to show that if

the operator ı has two boundary values at infinity , then N ( ) Jim - = ; to t2 where

N ...

What is the relationship between 0 ( t ) and the number of zeros of a

**solution**ofthe above equation ? G14 Use the result of the preceding exercise to show that if

the operator ı has two boundary values at infinity , then N ( ) Jim - = ; to t2 where

N ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero