# Tagged Questions

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 ...

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### Good books on theory of distributions

Hi all. I'm looking for english books with a good coverage of distribution theory. I'm a fan of Folland's Real analysis, but it only gives elementary notions on distributions. Thanks in advance.
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I'm learning a bit about the theory of distributions. What examples of distributions will help me develop good intuition? Definitions: Let $U$ be an open subset of $\mathbb{R}^n$. Write $C_c^\infty(... 5answers 3k views ### fourier transform of (real) exponential Is it possible to make sense, in distributional sense, of the Fourier transform of the exponential function (defined over the whole real line)? 1answer 471 views ### Is every distribution a linear combination of Dirac deltas? My question is whether Dirac-type distributions over an Abelian group define a basis of the Schwartz-Bruhat space$\mathcal{S}(G)^\times$of tempered distributions on$G$, so that any distribution$f\...
Let $G$ be a Hausdorff locally-compact Abelian group and $L^2(G)$ the Hilbert space of two-integrable complex functions on the group. Question. What would be natural vector space $\mathcal{R}$ ...
Question 1. Is there a nice or explicit way to describe the class of all distributions (generalized functions) $\mu$ on the $n$-sphere $S^n \subset \mathbb{R}^{n+1}$ for which the function  F(v) := \...