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Results tagged with schwartz-distributions
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user 165275
A distribution is a continuous linear functional on the space $\mathcal{C}^{\infty}_c$ of smooth (indefinitely differentiable) functions with compact support. Though they appeared in formal computations in the physics and engineering literature in the late $19^{th}$ century, their formal setting was brought up by the work of S. Sobolev and L. Schwartz in the middle of the $20^{th}$ century.
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Approximating compactly supported $L^2$ functions with Schwartz functions "from within"?
No, this is not possible, even if you define $\text{supp}(f)$ only as an equivalence class (up to a null set). For a counterexample take the characteristic function $f$ of a closed set $E$ of positive …
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