四元数分析中无界域上的Pompeiu公式和Plemelj公式
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摘要
引入修正的Cauchy核函数,证明四元数分析中无界域上的Pompeiu公式和Cauchy积分公式,再引入四元数分析中无界域上的Cauchy型积分,并考虑其边界性质,得到Plemelj公式.
By introducing the modified Cauchy kernel,the Pompeiu formula and Cauchy integral formula on unbounded domains in quaternion analysis was proved.The boundary properties of the Cauchy type integral operator over unbounded surface in quaternion analysis was studied,and Plemelj formula was obtained.
By introducing the modified Cauchy kernel,the Pompeiu formula and Cauchy integral formula on unbounded domains in quaternion analysis was proved.The boundary properties of the Cauchy type integral operator over unbounded surface in quaternion analysis was studied,and Plemelj formula was obtained.
引文
[1]GROSS F,TZE H C.Complex and quaternionic analyticity in chiral and gauge theories[J].Ann of Phys,1980,128:29-130.
[2]G¨URLEBECK K,SPR¨OSSIG W.Quaternionic analysis and elliptic boundary value problem[M].Boston:Birkha¨ouser,1990.
[3]SUDBERY A.Quaternionic Analysis[J],Math Proc Comb Phil Soc,1979,85:199-225.
[4]杨丕文.四元数分析中超球与双圆柱区域上的正则函数[J].系统科学与数学,1999,19(3):257-263.
[5]杨丕文.四元数分析中TGf算子的H¨older连续性和RiemannHilbert边值问题[J].数学学报,2003,46(5):993-998.
[6]杨丕文.四元数分析与偏微分方程[M].北京:科学出版社,2009.
[7]鄢盛勇.四元数分析中密度函数含参量的Cauchy型积分[J].西南师范大学学报:自然科学版,2011,36(4):78-82.
[8]鄢盛勇.四元数分析中TGf属于Lpv(G)的性质和Pompeiu公式[J].四川师范大学学报:自然科学版,2005,28(1):5-9.
[9]李觉友,杨丕文.四元数分析中k-左正则函数的性质及其Riemann边值问题[J].数学的实践与认识:2009,39(22):154-160.
[10]鄢盛勇.四元数分析中正则函数的非线性带位移边值问题[J].纯粹数学与应用数学:2012,28(4):475-482.
[11]鄢盛勇.四元数分析中正则函数向量的非线性边值问题[J].华南师范大学学报:自然科学版,2012,44(4):24-27.
[12]鄢盛勇.四元数分析中一类带共轭带位移的边值问题[J].广西民族大学学报:自然科学版,2011,17(3):49-53.
[13]谢永红,杨贺菊.Clifford分析中无界域上向量值函数的非线性边值问题[J].高校应用数学学报:2010,25(2):163-171.
[14]许娜,乔玉英.Clifford分析中无界域上正则函数带Haseman位移的边值问题[J].数学物理学报:2008,28A(5):846-855.
[15]KU M,DU J,WANG D.On generalization of MartinelliBochner integral formula using Clifford analysis[J].Adv Appl Clifford Alg,2010,20:351-366.
[2]G¨URLEBECK K,SPR¨OSSIG W.Quaternionic analysis and elliptic boundary value problem[M].Boston:Birkha¨ouser,1990.
[3]SUDBERY A.Quaternionic Analysis[J],Math Proc Comb Phil Soc,1979,85:199-225.
[4]杨丕文.四元数分析中超球与双圆柱区域上的正则函数[J].系统科学与数学,1999,19(3):257-263.
[5]杨丕文.四元数分析中TGf算子的H¨older连续性和RiemannHilbert边值问题[J].数学学报,2003,46(5):993-998.
[6]杨丕文.四元数分析与偏微分方程[M].北京:科学出版社,2009.
[7]鄢盛勇.四元数分析中密度函数含参量的Cauchy型积分[J].西南师范大学学报:自然科学版,2011,36(4):78-82.
[8]鄢盛勇.四元数分析中TGf属于Lpv(G)的性质和Pompeiu公式[J].四川师范大学学报:自然科学版,2005,28(1):5-9.
[9]李觉友,杨丕文.四元数分析中k-左正则函数的性质及其Riemann边值问题[J].数学的实践与认识:2009,39(22):154-160.
[10]鄢盛勇.四元数分析中正则函数的非线性带位移边值问题[J].纯粹数学与应用数学:2012,28(4):475-482.
[11]鄢盛勇.四元数分析中正则函数向量的非线性边值问题[J].华南师范大学学报:自然科学版,2012,44(4):24-27.
[12]鄢盛勇.四元数分析中一类带共轭带位移的边值问题[J].广西民族大学学报:自然科学版,2011,17(3):49-53.
[13]谢永红,杨贺菊.Clifford分析中无界域上向量值函数的非线性边值问题[J].高校应用数学学报:2010,25(2):163-171.
[14]许娜,乔玉英.Clifford分析中无界域上正则函数带Haseman位移的边值问题[J].数学物理学报:2008,28A(5):846-855.
[15]KU M,DU J,WANG D.On generalization of MartinelliBochner integral formula using Clifford analysis[J].Adv Appl Clifford Alg,2010,20:351-366.