- #1
tom_rylex
- 13
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Homework Statement
Show that if {x_k} is any sequence of points in space [tex] R^n [/tex] with [tex] |{x_k}| \rightarrow \infty [/tex], then [tex] \delta(x-x_k) \rightarrow 0 [/tex] weakly
Homework Equations
The Attempt at a Solution
I'm still trying to grasp the concept of weak convergence for distributions. It would appear that this function doesn't converge pointwise. The distribution on a test function is
[tex] \int \delta(x-x_k)\theta(x)dx = \theta(x_k)[/tex] Does the function converge weakly to zero because [tex] x_k [/tex] approaches infinity, and therefore would be outside of the region of support of any locally integrable test function?