The Stability of the Riemann Boundary Value Problem for Vector Valued M-Analytic Functions

  • Chuan-Gan Hu
  • Dan-Ping Zhang
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 2)


In this paper, certain boundary value problems are solved in a Banach space which is defined by vector-valued regular solutions of the systemm f x + M f y = 0 of elliptic partial differential equations, where M is a constant m × m matrix without real eigenvalues and f is an m × q matrix. The properties of the integral of Cauchy type for vector-valued M-analytic functions are discussed. Next, the representation of the solutions of the Riemann boundary value problem and its pertubed problem for vector-valued M-analytic functions are presented.


Singular Integral Equation Finite Order Polynomial Matrix Elliptic Partial Differential Equation Cauchy Type 
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  1. [1]
    Hill, G.N. : Elliptic systems in the plane with first order terms and constant coefficients. Comm. Part. Diff. Eq. 3 (1978), 947–977.Google Scholar
  2. [2]
    Hille E., Phillips, R.S.: Functional Analysis and Semi-Groups. Amer. Math. Soc. Colloq. Publ., Amer. Math. Soc, Providence, RI, 1957.Google Scholar
  3. [3]
    Hu, C.G. : The disturbance of vector-valued doubly-periodic Riemann boundary value problems. J. Math. Anal. Appl. 131 (1988), 373–391.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Hu, C.G. : Vector-valued boundary value problems of a class, Proceedings on International Conference on Integral Equations and Boundary Value Problems, ed. G.-C. Wen, Z. Zhao. World Scientific, Singapore, New Jersey, London, Hong Kong, 1991, 57–64.Google Scholar
  5. [5]
    Hu, C.G. : Elliptic functions and the stability of integral equations of a class in a locally convex space. Complex Variables Theory Appl. 24 (1994), 209–217.MathSciNetMATHGoogle Scholar
  6. [6]
    Hu, C.G. : Linear systems of a class in locally convex spaces, Complex analysis and its applications, ed. C.C. Yang et. al. Pitman Research Notes in Mathematics Series 305, Longman Scientific & Technical, Harlow, 1994, 90–199.Google Scholar
  7. [7]
    Hu, C.G., Yang,C.C.: Vector-valued functions and their applications. Kluwer Acad. Publ., Dordrecht, Boston, London, 1992.MATHGoogle Scholar
  8. [8]
    Lin W., Dai,D.: The Cauchy type integral for M-analytic function and its applications. Acta Math. Sci. 2 (1990), 149–166.MathSciNetGoogle Scholar
  9. [9]
    Lu, J.K. : Boundary value problems for analytic functions. World Scientific, Singapore, New Jersey, London, Hong Kong, 1993.MATHGoogle Scholar
  10. [10]
    Muskhelishvili,N.I. : Singular integral equations. Noordhoff, Groningen, 1953.MATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Chuan-Gan Hu
    • 1
  • Dan-Ping Zhang
    • 2
  1. 1.Department of MathematicsNankai UniversityTianjinChina
  2. 2.Research Section of MathematicsBeijing Institute of Machinery IndustryBeijingChina

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