## Linear Operators: Spectral theory |

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Page 1383

> 1; in Case C, the numbers {(n+})*, n > 0. In Case A, the (normalized)

eigenfunctions are {2^** sin not); in Case C, they are {2-” sin (n+})nt}. Thus, using

Theorem ...

**Consequently**, in Case A, the eigenvalues A are the numbers of the form (not)*, n> 1; in Case C, the numbers {(n+})*, n > 0. In Case A, the (normalized)

eigenfunctions are {2^** sin not); in Case C, they are {2-” sin (n+})nt}. Thus, using

Theorem ...

Page 1385

operator with kernel (ev-o-ev-o)e-V-W. — — , & 3 t, 2V-A (ev-At-e-V-X)e-V-A. —

— , t < 8. 2V-2 The matrix 0;(2) of Theorem 18 is

**Consequently**, by Theorem 3.16, if JoA # 0, the resolvent R(A; To) is an integraloperator with kernel (ev-o-ev-o)e-V-W. — — , & 3 t, 2V-A (ev-At-e-V-X)e-V-A. —

— , t < 8. 2V-2 The matrix 0;(2) of Theorem 18 is

**consequently**I I VT; 2V –2 () 0 ...Page 1387

the kernel sin vis(cos vot-Fi sin vo). & 3 t, J/A > 0, v2. in Vätscos V2s +i sin Väs

invasco votion vo). t 3 s, Jož > 0, VA in Visscos Vāt-i sin Vät sin votovo-isinvo), ...

**Consequently**, by Theorem 3.16, the resolvent R(A; T) is an integral operator withthe kernel sin vis(cos vot-Fi sin vo). & 3 t, J/A > 0, v2. in Vätscos V2s +i sin Väs

invasco votion vo). t 3 s, Jož > 0, VA in Visscos Vāt-i sin Vät sin votovo-isinvo), ...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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