I have a question about distributions. If we consider locally integrable function, then it is a limit of polynomials in the sense of $L^1$ convergence in any fixed compact set. Is every distribution also a limit of polynomials in the distribution topology? Is there any good reference about distribution theory? Thank you!
Asked
Active
Viewed 47 times
2
-
Yes, this is true, by the argument you sketch. Rudin, Functional Analysis, proves that every distribution is a derivative of a continuous function, this also implies your statement, by approximating the continuous functions by polynomials uniformly on compact sets. – Aug 04 '16 at 23:01
-
I see. Thank you very much! – Ale Aug 06 '16 at 17:21