## Linear Operators: Spectral operators |

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Page 2384

Q . E . D . For the spectral analysis of the operator T , we shall also need

asymptotic information on the “ second

u2o , that is , the

such a ...

Q . E . D . For the spectral analysis of the operator T , we shall also need

asymptotic information on the “ second

**solution**" of the differential equation To =u2o , that is , the

**solution**asymptotic to e - tut as t 00 . Since , in contrast to 01 ,such a ...

Page 2391

For use in what is to follow we record the formula for R ( a ; T ) obtained in the

proof of Lemma 4 and also observe that in constructing the kernel R ( s , t ; 2 ) in

Lemma 4 we may replace the particular “ second

in ...

For use in what is to follow we record the formula for R ( a ; T ) obtained in the

proof of Lemma 4 and also observe that in constructing the kernel R ( s , t ; 2 ) in

Lemma 4 we may replace the particular “ second

**solution**” oz ( t , d ) constructedin ...

Page 2394

On the other hand , since these two

have a linear relation 02 = aớı + 601 . ... Then there exists a

the equation to = u o , defined for 0 St < oo and for all sufficiently small u € P + ...

On the other hand , since these two

**solutions**are linearly independent , we musthave a linear relation 02 = aớı + 601 . ... Then there exists a

**solution**oz ( t , u ) ofthe equation to = u o , defined for 0 St < oo and for all sufficiently small u € P + ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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