Product solutions and separation of variables
A.J. Goldman · Journal of Research of the National Bureau of Standards Section B Mathematical Sciences · 1972
This paper consists of two independent notes, whose common features are (a) their concern with "product-form" functions and (b) their use of an abstract-algebra setting to isolate the essential features of the problems treated.The first note further generalizes the generalizations given by Ch u and Diaz (1965) of their observation that Euler's difference equation y(x+ 1)y(x) = f(x), whenf is of period 1, has the product•form solution y(x) = xf(x) .The second note fo rmalizes and rigoro usly proves the fact that a function is separable jointly in its variables iff it is separable in each individual variable.