michaelbriech
Mar26-09, 02:31 AM
1. The problem statement, all variables and given/known data
Find all u in D'(R) (distributions) such that xu = 0 in D'(R)
2. Relevant equations
3. The attempt at a solution
My first statement is that xu = 0 in distribution is the scalar product < xu, phi > = 0 where phi is any test function. Since it should be correct for ALL testfunctions this equals xu alone being equal to 0.
This must lead to that all solutions in D'(R) are captured with the dirac delta function?
/M
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
Find all u in D'(R) (distributions) such that xu = 0 in D'(R)
2. Relevant equations
3. The attempt at a solution
My first statement is that xu = 0 in distribution is the scalar product < xu, phi > = 0 where phi is any test function. Since it should be correct for ALL testfunctions this equals xu alone being equal to 0.
This must lead to that all solutions in D'(R) are captured with the dirac delta function?
/M
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution