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Positive resonances and the limiting amplitude principle

✍ Scribed by D. Eidus

Publisher
Springer
Year
1986
Tongue
English
Weight
113 KB
Volume
12
Category
Article
ISSN
0377-9017

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✦ Synopsis

We define the positive resonance points of self-adjoint operators without using the analytical continuation of corresponding resolvents and show that the limiting amplitude principle for the abstract wave equation does not take place in general, if m2 = 2, where co is the disturbing frequency and 2 is the resonance point. The asymptotics of corresponding solutions as t --, ~ are obtained, which imply the growth of the oscillation amplitude as t ~, 0 < fl < 1, or as In t, t ~ oo.

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