- #1
math771
- 204
- 0
Hi there,
I am also familiar with Hilbert spaces and Functional Analysis and I find your question very interesting. I agree that the Fourier transform is a powerful tool for analyzing LTI systems and diagonalizing the convolution operator. As for your question about whether the same can be shown for the operator convolution, I believe it is possible.
I did a quick search and found a reference that might be helpful for you. It's a paper titled "Eigenfunctions of Convolution Operators" by A. B. Aleksandrov. I haven't read it in depth, but from the abstract it seems to address your question.
I hope this helps! Let me know if you have any other questions or if you find any other useful references.