ZHANG Jian-yuan, ZHAO Shu-fen, HAN Yan. Riemann’s Boundary Value Problem of K-Analytic Functions[J]. Applied Mathematics and Mechanics, 2014, 35(7): 805-814. doi: 10.3879/j.issn.1000-0887.2014.07.010
Citation: ZHANG Jian-yuan, ZHAO Shu-fen, HAN Yan. Riemann’s Boundary Value Problem of K-Analytic Functions[J]. Applied Mathematics and Mechanics, 2014, 35(7): 805-814. doi: 10.3879/j.issn.1000-0887.2014.07.010

Riemann’s Boundary Value Problem of K-Analytic Functions

doi: 10.3879/j.issn.1000-0887.2014.07.010
Funds:  The National Natural Science Foundation of China(11061028)
  • Received Date: 2013-11-28
  • Rev Recd Date: 2014-05-27
  • Publish Date: 2014-07-15
  • First, the concepts of the (piecewise) K-analytic function and the Cauchy type K-integral were introduced, and some properties of the Cauchy type K-integral were studied through K-symmetry transformation. Then, with the function index of the curve and the properties of the Cauchy type K-integral, the solvable conditions and the solution expressions for the Riemann’s boundary value problem of the K-analytic function as well as the relationship between the solutions and the index were obtained. Since both the analytic functions and the conjugate analytic functions are special cases of the K-analytic functions, the present conclusions generalize many known related results of them.
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