## Linear Operators: Spectral theory |

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Page 1301

They are clearly linearly

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

**independent**of the set A , ,. . . , 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 = 0 square integrable at a or b when I ( a ) + 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 ( 1 – 2 )0 = 0 square integrable at a or b when I ( a ) + 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

) = 0 , i = 1 , . . . , k ; i . e . , T is the restriction of T ( T ) ( cf . Definition 2 . 8 ) to the ...

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 ; ( t) = 0 , i = 1 , . . . , k ; i . e . , T is the restriction of T ( T ) ( cf . Definition 2 . 8 ) to the ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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