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Results tagged with schwartz-distributions
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user 18936
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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Constrain representation of tempered distribution
This is a follow-up to this question.
Let $T$ be a tempered distribution on $\mathbb{R}^d$.
Then there is a multiindex $\alpha \in \mathbb{N}_0^d$, an $n \in \mathbb{N}_0$ and a bounded continuous fu …
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Prove that a given distribution is tempered
Suppose I have a distribution $E$ such that $\phi \ast E$ is square-integrable for all $\phi \in C_c^\infty \left( \mathbb{R}^d \right)$. Is it possible to prove that $E$ is tempered? It seems plausib …
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Feynman path integral and Wilsonian renormalization
Everything below is to be viewed in the Euclidean setting with $d$ dimensions and all measures are understood to be Borel measures.
The usual problem of Quantum Field Theory is to make sense of Feynma …
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