this preprint answers that in the affirmative
otoh, (x, y) -> 1/(x-y) does not answer this question at all. you can argue that the preprint does so "via the infinite series in an operation" (which I have no idea what that means; surely if exp(x) qualifies then so must 1/(x-y) if we pick a monomial basis?) but ¯\_(ツ)_/¯
now, do I think that this is groundbreaking magical research (as I'm currently seeing on twitter) no... But it's neat!