Quadrature Formulas of Quasi-Interpolation Type for Singular Integrals with Hilbert Kernel

  title={Quadrature Formulas of Quasi-Interpolation Type for Singular Integrals with Hilbert Kernel},
  author={Du Jin-yuan},
  journal={Journal of Approximation Theory},
  • Du Jin-yuan
  • Published 1998
  • Mathematics
  • Journal of Approximation Theory
  • In this paper, we first establish quadrature formulas of trigonometric interpolation type for proper integrals of periodic functions with periodic weight, then we use the method of separation of singularities to derive those for corresponding singular integrals with Hilbert kernel. The trigonometric precision, the type, the estimate of the remainder, and the convergence of each quadrature formula derived here are also established. 
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