L[x0,x1,...,xn;f+g]=?=L[x0,x1,...,xn;f] + L[x0,x1,...,xn;g] where f and g are ordinary functions, not neccessarily polynomials......
closed as unclear what you're asking by TheSimpliFire, i. m. soloveichik, Chris Godsil, José Carlos Santos, Mohammad Riazi-Kermani Feb 20 '18 at 0:03
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If $L[x_0, \ldots, x_n; f]$ means a polynomial of degree $ \le n$ that has the same values as $f$ at $x_0, \ldots, x_n$, then yes, this is true.