Abstract
Consider the real Clifford algebra \({\mathbb{R}_{0,n}}\) generated by e 1, e 2, . . . , e n satisfying \({e_{i}e_{j} + e_{j}e_{i} = -2\delta_{ij} , i, j = 1, 2, . . . , n, e_{0}}\) is the unit element. Let \({\Omega}\) be an open set in \({\mathbb{R}^{n+1}}\) . u(x) is called an h-regular function in \({\Omega}\) if
where \({D_x = \sum\limits_{i=0}^{n} e_{i}\partial_{xi}}\) is the Dirac operator in \({\mathbb{R}^{n+1}}\) , and \({\widehat{u}(x) = \sum \limits_{A} (-1)^{\#A}u_{A}(x)e_{A}, \#A}\) denotes the cardinality of A and \({h = \sum\limits_{k=0}^{n} h_{k}e_{k}}\) is a constant paravector. In this paper, we mainly consider the Hilbert boundary value problem (BVP) for h-regular functions in \({\mathbb{R}_{+}^{n+1}}\) .
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Supported by NNSF of China (11171260) and RFDP of Higher Education of China (20100141110054)
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Zhongwei, S., Jinyuan, D. & Ping, D. The Left Hilbert BVP for h-Regular Functions in Clifford Analysis. Adv. Appl. Clifford Algebras 23, 519–533 (2013). https://doi.org/10.1007/s00006-012-0374-0
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DOI: https://doi.org/10.1007/s00006-012-0374-0