A new property of reproducing kernels for classical orthogonal polynomials

We exhibit a second-order differential operator commuting with the reproducing kernel $\text{∑}{}_{\mathrm{n\; ?\; 0}}{}^{\mathrm{T}}\text{φ}{}_{\mathrm{n}}\text{(λ)}\text{φ}{}_{\mathrm{n}}\text{(μ)}\text{h}{}_{\mathrm{n}}$ each time that {φ_n(λ)} is one of the classical orthogonal polynomials: Jacobi, Laguerre, Hermite and Bessel. This is the analog of a known property in the study of time and band-limited signals.