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Suppose I have a linear operator $L$ s.t. $Ly(x-a)=\exp(-iax)Ly(x)$ and $L^2y(x)=ky(-x)$ where $a, k\in \mathbb R.$ Then what is $L^2y(x-a)$? May be it is really straightforward, but I don't know how to combine them!  Thank you.

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    Where is $L$ supposed to be defined? (it seems to be a space of function, but I want to be sure)2011-11-16
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    @DavideGiraudo: Yes, it is the space of functions.2011-11-16

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