## Linear Operators: Spectral theory |

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Page 1550

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

that every solution of the equation q * f = 0 is of class L ( I ) ( p - 1 + q - 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 tf = 0 is of class L , ( I ) and

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

Page 1557

Suppose that q is bounded below , and suppose that a does not belong to the

essential spectrum of t . Let f be a square - integrable solution of the equation ( 2 -

1 ) ...

**Prove**that the point à belongs to the essential spectrum of t . G20 ( Wintner ) .Suppose that q is bounded below , and suppose that a does not belong to the

essential spectrum of t . Let f be a square - integrable solution of the equation ( 2 -

1 ) ...

Page 1560

G31

) , 0 ) ds = 0 ( t3 log2 t ) , then the operator t has no boundary values at infinity .

G32 ( Hartman and Wintner ) Suppose q is negative and differentiable . Let N ( t )

...

G31

**Prove**the following refinement of the result of Exercise G19 ( d ) : if x ( - 9 ( s) , 0 ) ds = 0 ( t3 log2 t ) , then the operator t has no boundary values at infinity .

G32 ( Hartman and Wintner ) Suppose q is negative and differentiable . Let N ( t )

...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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