On Pólya's functional equation
Juan-Miguel Gracia · International Journal of Mathematical Education in Science and Technology · 1987
Let Y be a continuous matrix valued function defined on R, verifying the functional equation Y(s +t) = Y(s) Y(t) for all real s, t. This paper corrects certain mistakes found in an earlier elementary proof that Y is differentiable at 0. Also, reference is made to some relations of this equation with one‐parameter groups, with Chapman—Kolmogorov equation in Markov processes, with combinatorics, and with a characterization of the solutions of the constant coefficient homogeneous linear differential equations.