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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 3, Pages 503–514
(Mi smj1977)
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This article is cited in 1 scientific paper (total in 1 paper)
On the subspace $L((x\land y)^m)$ of $S^m(\land^2\mathbb R^4)$
V. Yu. Gubarev Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk
Abstract:
We take the exterior power $\mathbb R^4\land\mathbb R^4$ of the space $\mathbb R^4$, its $m$th symmetric power $V=S^m(\land^2\mathbb R^4)=(\mathbb R^4\land\mathbb R^4)\vee(\mathbb R^4\land\mathbb R^4)\vee\cdots\vee(\mathbb R^4\land\mathbb R^4)$, and put $V_0=L((x\land y)\vee\cdots\vee(x\land y)\colon x,y\in\mathbb R^4)$. We find the dimension of $V_0$ and an algorithm for distinguishing a basis for $V_0$ efficiently. This problem arose in vector tomography for the purpose of reconstructing the solenoidal part of a symmetric tensor field.
Keywords:
symmetric power of a space, exterior power of a space.
Received: 03.04.2008
Citation:
V. Yu. Gubarev, “On the subspace $L((x\land y)^m)$ of $S^m(\land^2\mathbb R^4)$”, Sibirsk. Mat. Zh., 50:3 (2009), 503–514; Siberian Math. J., 50:3 (2009), 395–404
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https://www.mathnet.ru/eng/smj1977 https://www.mathnet.ru/eng/smj/v50/i3/p503
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Abstract page: | 517 | Full-text PDF : | 76 | References: | 41 | First page: | 2 |
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