Some properties of holomorphic Cliffordian functions and boundary value properties of the Cauchy type integral in unbounded domain
In the first place,the left and right holomorphic Cliffordian functions are defined in Euclidean space and with values in real Clifford algebra.Then some spacial properties of holomorphic Cliffordian functions are discussed by way of the properties of regular functions.With the help of the first class of Quasi-Permutation,the equal conditions are proved from the angle of regular functions,which build the relations between regular functions and holomorphic Cliffordian functions.And then,the extension theorem is discussed based on the Cauchy type integral formula and the Plemelj formula in the bounded domain using some small techniques.Finally,the Cauchy type integral is defined on unbounded domains,and it is proved be convergent under the meaning of Cauchy principal value.And the Plemelj formula is discussed by way of some significant integral estimation and some methods above.
holomorphic Cliffordian functionsCauchy type integralCauchy principal valuePlemelj formula
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维普
