A generalized function whose kth derivative is 0

[e(ho0n3]

Homework Statement

Let f be a distribution on R and suppose that its kth derivative is 0. Prove that f is a polynomial.

2. The attempt at a solution
I honestly haven't a clue how to start. If I could treat f like a "regular" function, this would so easy.

 

[estro]

Maybe worth to try integrating k times?=)

 

[e(ho0n3]

I believe integration does not exist for distributions so that will not work.

 

[nonequilibrium]

Well the first question to ask it "what does the derivative of a distribution mean?", i.e. what's the definition of the derivative of a distribution?

 

[e(ho0n3]

The derivative f' is the distribution defined by (f', g) = -(f, g'), where g is any test function.