MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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

In some situations we have access to a representation like this:

$ f(x,y) = \sum_i u_i(x) v_i(y) $

What is this called? (I know when you jam this into PDE get to call it 'separation of variables' but I'm sure it's got a different name in pure math).

share|cite|improve this question
The function $f$ is called separable in some other circumstances too. Like my masters thesis and a number of game theory references therein (none of which have anything to do with PDE). – Noah Stein Jan 25 '13 at 23:14
up vote 2 down vote accepted

This paper calls it "separable of rank $n$" if $n$ is the number of terms in the sum. If the sum is an infinite one, the condition is very weak (for example it includes all functions with a convergent Taylor expansion).

share|cite|improve this answer

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.