## Linear Operators: Spectral theory |

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Page 1550

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

that every solution of the equation * 4 = 0 is of class L , ( I ) ( p - 1 + q - 1 = 1 ) .

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

that every solution of the equation * 4 = 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 7 . Let f be a square - integrable solution of the equation ( 2

- 1 ) ...

**Prove**that the point a 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 7 . Let f be a square - integrable solution of the equation ( 2

- 1 ) ...

Page 1568

if t ) dt 21 . H13 Suppose that ( 1 + t ) g ( t ) | dt < 0 .

continuous spectrum of every self adjoint extension of the operator To ( t ) .

**Prove**that a self adjoint extension of the operator has a negative eigenvalue onlyif t ) dt 21 . H13 Suppose that ( 1 + t ) g ( t ) | dt < 0 .

**Prove**that the origin lies in thecontinuous spectrum of every self adjoint extension of the operator To ( t ) .

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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