Energy-preserving convolution kernel?
I think any allpass filter should do that. Since they only change phase and not amplitude in the frequency domain, the time domain energy remains unchanged per Parseval's theorem.
$$\sum x[n]^2 = \sum |X(k)|^2$$
An all pass only changes the phase of $X(k)$ so total energy is maintained.
You could argue that an allpass is an IIR filter, so it's not suitable to be a convolution kernel (which implies FIR). But some allpass filters are FIR (delays) and you can always truncate an allpass IIR impulse response to the &quot;desired precision&quot;.