The Riemann Hilbert problem for generalized Q-holomorphic functions

In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions.

The Riemann Hilbert problem for generalized Q-holomorphic functions

In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions.

___

  • Begehr, H. and Gilbert, R. P.: On Riemann boundary value problems for certain linear elliptic systems in the plane, J. Differential Equations 32, 1 – 14 (1979).
  • Begehr, H. and Gilbert, R. P.: Transformations, Transmutations and Kernel Functions, I, II, Longman, Harlow , 1993.
  • Bers, L.: Theory of Pseudo-Analytic Functions, Inst. Math. Mech., New York University (Lecture Notes), 1953.
  • Bojarski˘ı, B. V.: Theory of generalized analytic vectors (in Russian), Ann. Polon. Math., 17 , 281 – 230 (1966).
  • Douglis, A.: A function theoretic approach to elliptic systems of equations in two variables, Comm. Pure Appl. Math., 6 , 259–289 (1953).
  • Gilbert, R. P.: Constructive Methods for Elliptic Equations, Lectures Notes in Math. 365, Berlin, Springer 1974.
  • Gilbert, R. P.: Pseudohyperanalytic function theory, In: Proc. of conf. Function Theoretic Methods in Differential Equations (Bonn 1972, ed.:St. Ruscheweyh). Bonn Berichte Ges. Math. Datenverarbeit, 77, 53 – 63 (1973).
  • Gilbert, R. P. and Buchanan, J. L.: First Order Elliptic Systems. A Function Theoretic Approach. Orlando (FL), Academic Press 1983.
  • Gilbert, R. P. and Hile, G. N.: Generalized hypercomplex function theory, Trans. Amer. Math. Soc., 195 , 1 – 29 (1974).
  • Gilbert, R. P. and Hile, G. N.: Hypercomplex function theory in the sense of L. Bers, Math. Nachr., 72 , 187 – 200 (1976).
  • Haack, W. and Wendland, W.: Lectures on Partial and Pfaffian Differential Equations, Oxford, Pergamon Press Hile, G. N.: Function theory for generalized Beltrami systems, Comp. Math., 11 , 101 – 125 (1982).
  • Hızlıyel, S. and C¸ a˘glıyan, M.: Generalized Q-holomorphic functions, Complex Variables , 49 , 427 – 447 (2004).
  • Hızlıyel, S. and C¸ a˘glıyan, M.: Pseudo Q-holomorphic functions, Complex Variables, 49 , 941 – 955 (2004).
  • Hızlıyel, S. and C¸ a˘glıyan, M.: A Dirichlet problem for a matrix equation, Complex Variables and Elliptic Equations, , 575 – 588 (2007).
  • Vekua, I. N.: Generalized Analytic Functions, London, Pergamon Press 1962.
  • Sezayi HIZLIYEL, Mehmet C¸ A ˘GLIYAN Uluda˘g University, Art and Science Faculty Deparment of Mathematics G¨or¨ukle-Bursa, TURKEY e-mail : hizliyel@uludag.edu.tr