# Questions tagged [schwartz-distributions]

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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### Characterizing geometrically Schwartz Kernels of pseudodifferential operators on a compact manifold

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### Defining the value of a distribution at a point

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### Interchanging Integration Order involving Fourier Transform

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### Fourier inversion formula for compactly supported distributions

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### Fourier transform of a Lorentz invariant generalized function

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### Fourier Restriction: extension operator identity

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### Extension of Valdivia-Vogt isomorphism from $\mathscr{D}(K)$ to $\mathscr{E}'(K)$

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### Entire analytic functions with entire analytic Fourier transform, and corresponding distributions

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### Delta-distribution composed with a function from the Fourier representation

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### Convolution with Schwartz class function

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### is this explicit linear operator hypo-elliptic

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### Is convolution jointly continuous on $\mathcal{E}'$?

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### Trace on $\mathcal{S}(\mathbb{R}^k) \mathbin{\hat{\otimes}_\pi} \mathcal{S}'(\mathbb{R}^k)$

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### Covergent net in $\mathcal{E}'(\mathbb{R})$ implies bounded?

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