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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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Representation of an operator on a generalized eigenfunction

This is a cross-post from: https://math.stackexchange.com/questions/4651664/representation-of-an-operator-on-a-generalized-eigenfunction Suppose we have an (essentially) self adjoint operator $L$ acti …
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