Positive resonances and the limiting amplitude principle |
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Authors: | D Eidus |
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Institution: | (1) School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel |
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Abstract: | 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 2 = , where is the disturbing frequency and is the resonance point. The asymptotics of corresponding solutions as t are obtained, which imply the growth of the oscillation amplitude as t
, 0<<1, or as ln t, t . |
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Keywords: | |
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