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Distribution theory

1. Homework Statement

Find all u in D'(R) (distributions) such that xu = 0 in D'(R)

2. Homework 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. Homework Statement



2. Homework Equations



3. The Attempt at a Solution
 

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