## Linear Operators: Spectral theory |

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Page 1301

They are clearly linearly

it would follow that r has a boundary value at a which is

, ..., An-1, and hence has at least n+1

They are clearly linearly

**independent**. If the assertion of the corollary were false,it would follow that r has a boundary value at a which is

**independent**of the set A0, ..., An-1, and hence has at least n+1

**independent**boundary values at a.Page 1306

The following table gives the number of linearly

= 0 square integrable at a or b when Jo (2) # 0. There are four possibilities as

shown by the discussion above. Number of linearly

The following table gives the number of linearly

**independent**solutions of (r–A) a= 0 square integrable at a or b when Jo (2) # 0. There are four possibilities as

shown by the discussion above. Number of linearly

**independent**solutions ...Page 1311

The operator T = T(t) will be an operator obtained from t by the imposition of a set,

which may be vacuous, of k linearly

= 1,..., k; i.e., T is the restriction of Ti(r) (cf. Definition 2.8) to the submanifold of ...

The operator T = T(t) will be an operator obtained from t by the imposition of a set,

which may be vacuous, of k linearly

**independent**boundary conditions B,(f) = 0, i= 1,..., k; i.e., T is the restriction of Ti(r) (cf. Definition 2.8) to the submanifold of ...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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