On global smoothness preservation in complex approximation

Volume 79 / 2002

George A. Anastassiou, Sorin G. Gal Annales Polonici Mathematici 79 (2002), 199-205 MSC: 30E10, 41A10, 41A25, 41A63, 41A99. DOI: 10.4064/ap79-3-1


By using the properties of convergence and global smoothness preservation of multivariate Weierstrass singular integrals, we establish multivariate complex Carleman type approximation results with rates. Here the approximants fulfill the global smoothness preservation property. Furthermore Mergelyan's theorem for the unit disc is strengthened by proving the global smoothness preservation property.


  • George A. AnastassiouDepartment of Mathematical Sciences
    University of Memphis
    Memphis, TN 38152, U.S.A.
  • Sorin G. GalDepartment of Mathematics
    University of Oradea
    Str. Armatei Romane 5
    3700 Oradea, Romania

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