On a theorem of S. Bernstein-Widder
J. D. Tamarkin · Transactions of the American Mathematical Society · 1931
The present note is merely a comment to the preceding paper by D. V. Widder, and was suggested by the reading of its manuscript. It gives a simplified proof of the following important theorem discovered recently by S. Bernstein, and subsequently, but independently, by Widder, whose proof is based upon entirely different principles. THEOREM. A necessary and sufficient condition that the function f(x) should be completely monotonic in the interval c <x < so is that