## Linear Operators: Spectral theory |

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Page 1550

Bellman ) Suppose that every solution of the equation of = 0 is of class L , ( I ) and

that every solution of the equation q * f = 0 is of class Lg ( I ) ( p - 1 + 9 + 1 = 1 ) .

**Prove**that the essential spectrum of the operator r in L ( I ) is the empty set . E8 (Bellman ) Suppose that every solution of the equation of = 0 is of class L , ( I ) and

that every solution of the equation q * f = 0 is of class Lg ( I ) ( p - 1 + 9 + 1 = 1 ) .

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solution . ...

) Suppose q is non - positive , and let tn be the n - th zero of a solution of the

equation tf ...

**Prove**that the equation g ' ' ( t ) -92 ( t ) g ( t ) = 0 has a square - integrablesolution . ...

**Prove**the following : ( a ) If N ( t ) > 1 , then Soó 19 ( 8 ) | ds > 41-1 ( b) Suppose q is non - positive , and let tn be the n - th zero of a solution of the

equation tf ...

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of t contains the positive semi - axis . ( Hint : Apply Theorem 7.1 . ) G41 Suppose

that the function q is bounded below . Suppose that the origin belongs to the ...

**Prove**that | ( 1-7 ) n ] = 0 ( V ( bom - a , ) ) . ( b )**Prove**that the essential spectrumof t contains the positive semi - axis . ( Hint : Apply Theorem 7.1 . ) G41 Suppose

that the function q is bounded below . Suppose that the origin belongs to the ...

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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

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