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# Hardy-Hodge Decomposition of Vector Fields in R$^{n}$

Abstract : We prove that a R^(n+1)-valued vector field on R^n is the sum of the traces of two harmonic gradients, one in each component of R^(n+1) \ R^n , and of a R^n-valued divergence free vector field. We apply this to the description of vanishing potentials in divergence form. The results are stated in terms of Clifford Hardy spaces, the structure of which is important for our study.
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https://hal.inria.fr/hal-01462960
Contributor : Laurent Baratchart Connect in order to contact the contributor
Submitted on : Tuesday, February 14, 2017 - 12:49:27 PM
Last modification on : Wednesday, September 14, 2022 - 5:42:26 PM
Long-term archiving on: : Monday, May 15, 2017 - 12:22:55 PM

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### Citation

Laurent Baratchart, Pei Dang, Tao Qian. Hardy-Hodge Decomposition of Vector Fields in R$^{n}$. Transactions of the American Mathematical Society, 2018, 370 (3), pp.2005 - 2022. ⟨10.1090/tran/7202⟩. ⟨hal-01462960⟩

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