What are the entries of a diagonal operator?

I had been thinking of operators in the kernel sense, that is,
$$
(K u)(x) = \int_a^b K(x,y) u(y) dy
$$
So that K[x,y] is equivalent to K(x,y).

But then we are using diagonal operators. One might expect QuasiDiagonal(one.(Inclusion(-1...1))) to be the identity operator, and thats essentially how we've been using it. The issue is that the identity operator corresponds to K(x,y) = δ(y-x) so is actual infinite on the diagonal.

Is this the convention we want? E.g., QuasiDiagonal(sqrt.(1-x.^2))[0.1,0.1] == ∞?

Start with the operator and kernel convention described in the issue, especially QuasiDiagonal(...)[x,y] and the identity example. Determine the intended semantics for diagonal entries, including whether the identity and sqrt example should produce finite values or infinity. Done when the convention is agreed and reflected in the relevant behavior or tests.