User debraj chakrabarti - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T19:14:28Z http://mathoverflow.net/feeds/user/1480 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/4706/what-examples-of-distributions-should-i-keep-in-mind/4714#4714 Answer by Debraj Chakrabarti for What examples of distributions should I keep in mind? Debraj Chakrabarti 2009-11-09T06:00:33Z 2009-11-09T06:00:33Z <p>Two comments:</p> <p>(1) Every distribution can be locally represented as a (distributional) partial derivative of a continuous function. For example, for the dirac delta at 0, we can start from the function which is 0 for negative x, and equal to x for positive x and take two derivatives. Therefore, it is important to understand that not all distributions are made equal -- the more complicated ones are made by taking more derivatives of continuous functions.</p> <p>(2) Some examples to definitely keep in mind (to emphasize the subtleness of the notion) while thinking about distributions are the principal value p.v $\frac{1}{x}$ and the pseudofunctions p.f. $\frac{1}{x^n}$</p>