Clifford分析中无界域上Isotonic函数的Plemelj公式
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摘要
定义了无界域上Isotonic函数的Cauchy型积分和Cauchy主值积分,考虑了其边界性质,得到了无界域上Isotonic函数的Plemelj公式.
In this paper, We define the Cauchy-type integral, and Cauchy principal value for the Isotonic functions on unbounded domains in Clifford Analysis, discuss some boundary properties of the Cauchy-type integral operator, and obtain the Plemelj formulae for the Isotonic functions on unbounded domains.
In this paper, We define the Cauchy-type integral, and Cauchy principal value for the Isotonic functions on unbounded domains in Clifford Analysis, discuss some boundary properties of the Cauchy-type integral operator, and obtain the Plemelj formulae for the Isotonic functions on unbounded domains.
引文
[1] Brackx F, Delanghe R., Sommen F. Clifford Analysis[M]. London:Pitman Books Ltd, 1982.
[2] Guerlebeck K, Sproessing W. Quaternionic and Clifford calculus for physicists and engineers[M].Wiley:Chichester, 1998.
[3] Sommen F, Pena-Pena D. Martinelli-Bochner formula using Clifford analysis[J]. Arch Math, 2007,88:358-363.
[4] Abreu-Blaya R, Bory-Reyes J. A Martinelli-Bochner formula on fractal domains[J]. Arch Math,2009, 92:335-343.
[5] Abreu-Blaya R, Bory-Reyes J, Pena-Pena D, Sommen F. A Holomorphic Extension Theorems using Clifford analysis[J]. Complex Anal Oper Theory, 2011, 5:113-130.
[6] Abreu-Blaya R, Bory-Reyes J, Pena-Pena D, Sommen F. Holomorphic extension theorems in lipschitz domains of C~2[J]. Adv Appl Clifford Alg, 2010, 20:1-12.
[7] Abreu-Blaya R, Bory-Reyes J, Brackx F, De Schepper H, Sommen F. A Hermitian Cauchy formula on a domain with fractal boundary[J]. J Math Anal Appl, 2010, 369:273-282.
[8] Abreu-Blaya R, Bory-Reyes J, Pena-Pena D, Sommen F. Biregular extendability via isotonic Clifford analysis[J]. Math Meth Appl Sci, 2010, 33:384-393.
[9]鄢盛勇.Clifford分析中Isotonic函数带位移的非线性边值问题[J].重庆师范大学学报(自然科学版):2013, 30(2):34-38.
[10]库敏,杜金元,王道顺.Clifford分析中Isotonic柯西型积分的边界性质[J].数学学报,2011,54(2):177-186.
[11]鄢盛勇.四元数分析中无界域上的Pompeiu公式和Plemelj公式[J].兰州理工大学学报,2014, 40(1):155-159.
[12]鄢盛勇.四元数分析中无界域上正则的数的线性边值问题[J].西南师范大学学报(自然科学版):2015,40(2):20-25.
[13] Xu N, Du J Y. Plemelj formula for Cauchy type integral on certain distinguished boundary in universal Clifford analysis[J]. Wuhan Univ J of Nature Sciences, 2007, 12(3):385-390
[14]贺福利,库敏,杜金元.旋量值的数的Plemelj公式[J].数学年刊,2015,36A(4):429-438.
[15] Guerlebeck K, Kahler U, Ryan J. Clifford analysis over unbounded domains[J]. Adv in Appl Math,1997, 19:216-236.
[16] Ku M. Integral formula of isotonic functions over unbounded domain in clifford analysis[J]. Adv Appl Clifford Alg, 2010, 20:57-70.
[17] Ku M, Du J Y, Wang D S. On Generalization of martinelli-bochner integral formula using clifford analysis[J]. Adv Appl Clifford Alg, 2010, 20:351-366.
[2] Guerlebeck K, Sproessing W. Quaternionic and Clifford calculus for physicists and engineers[M].Wiley:Chichester, 1998.
[3] Sommen F, Pena-Pena D. Martinelli-Bochner formula using Clifford analysis[J]. Arch Math, 2007,88:358-363.
[4] Abreu-Blaya R, Bory-Reyes J. A Martinelli-Bochner formula on fractal domains[J]. Arch Math,2009, 92:335-343.
[5] Abreu-Blaya R, Bory-Reyes J, Pena-Pena D, Sommen F. A Holomorphic Extension Theorems using Clifford analysis[J]. Complex Anal Oper Theory, 2011, 5:113-130.
[6] Abreu-Blaya R, Bory-Reyes J, Pena-Pena D, Sommen F. Holomorphic extension theorems in lipschitz domains of C~2[J]. Adv Appl Clifford Alg, 2010, 20:1-12.
[7] Abreu-Blaya R, Bory-Reyes J, Brackx F, De Schepper H, Sommen F. A Hermitian Cauchy formula on a domain with fractal boundary[J]. J Math Anal Appl, 2010, 369:273-282.
[8] Abreu-Blaya R, Bory-Reyes J, Pena-Pena D, Sommen F. Biregular extendability via isotonic Clifford analysis[J]. Math Meth Appl Sci, 2010, 33:384-393.
[9]鄢盛勇.Clifford分析中Isotonic函数带位移的非线性边值问题[J].重庆师范大学学报(自然科学版):2013, 30(2):34-38.
[10]库敏,杜金元,王道顺.Clifford分析中Isotonic柯西型积分的边界性质[J].数学学报,2011,54(2):177-186.
[11]鄢盛勇.四元数分析中无界域上的Pompeiu公式和Plemelj公式[J].兰州理工大学学报,2014, 40(1):155-159.
[12]鄢盛勇.四元数分析中无界域上正则的数的线性边值问题[J].西南师范大学学报(自然科学版):2015,40(2):20-25.
[13] Xu N, Du J Y. Plemelj formula for Cauchy type integral on certain distinguished boundary in universal Clifford analysis[J]. Wuhan Univ J of Nature Sciences, 2007, 12(3):385-390
[14]贺福利,库敏,杜金元.旋量值的数的Plemelj公式[J].数学年刊,2015,36A(4):429-438.
[15] Guerlebeck K, Kahler U, Ryan J. Clifford analysis over unbounded domains[J]. Adv in Appl Math,1997, 19:216-236.
[16] Ku M. Integral formula of isotonic functions over unbounded domain in clifford analysis[J]. Adv Appl Clifford Alg, 2010, 20:57-70.
[17] Ku M, Du J Y, Wang D S. On Generalization of martinelli-bochner integral formula using clifford analysis[J]. Adv Appl Clifford Alg, 2010, 20:351-366.