eigen functions of LTI systems

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6sbtixjo

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For an LTI system, exponentials e^st are well known eigen functions. But say if we have in general a^st as the input to an LTI system, the output will be scaled by a function A(s) similar to Laplace transform where now, the instead of e^(-st) we will have a^(-st). So is it now correct to call a^st to be an eigen function of an LTI system?
 

In that sense a^(-st) could be called as an eigen function and it could be written as e^(-st*ln(a)) so it only amounts to a little change of scale. Do you have any particular reasons to do this
 

Thanks. I just was thinking about why do we concern so much about exponentials (e^st) while a^(st) could be a more general representation, where a=e would give e^st.
 

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