MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $f(\lambda)=\int_0^\infty e^{-\lambda s} F(ds)$, where $F$ is the distribution of a positive random variable. Suppose I know the value of $f(n)$ for $n=0,1,2,\cdots$. Is this enough to uniquely determine $f(\lambda)$ in its domain of convergence (DOC)?

Since the Laplace transform is analytic in its DOC, knowledge of $f(\lambda$) on a line segment uniquely determines $f(\lambda)$ on its domain. But, knowledge of the value of an analytic function at a countably infinite number of points does not, in general, determine the function throughout its domain. I was hoping that, analyticity + the fact that $f(\lambda)$ is a Laplace transform would be enough to analytically continue $f(\lambda)$ from a countably infinite set of points.

It would seem like the fact that $f(\lambda)$ is positive, decreasing and convex might be useful.

share|cite|improve this question
up vote 2 down vote accepted

A uniqueness theorem you formulated is proved here: for the case where $F$ satisfies the Lipschitz condition.

share|cite|improve this answer
Perfect! I can't tell you how much this helps my paper. – psyduck Mar 16 '12 at 19:31

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.