This question was asked already on Stack Exchange under https://math.stackexchange.com/q/1114095 . It might be not on a research level, but as it could not be answered on Stack Exchange, I hope for your kind hints / references:
What do we know about the spectrum of the convolution operator in a bounded domain $D \subset \mathbb{R}$:
$$J∗u=\int_D J(x−y)u(y)dy$$
where $u$ is an $L^1(D)$ - function.
Which methods can I use to determine the spectrum?
Any hints/references are greatly appreciated.
Thank you!
