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Trigonometric Induced Multivariate Smooth Gauss–Weierstrass Singular Integrals Approximation

Author

Listed:
  • George A. Anastassiou

    (Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA)

Abstract

In this article, we employ the uniform and L p , 1 ≤ p < ∞ approximation properties of general smooth multivariate singular integral operators over R N , N ≥ 1 . It is a trigonometric relief approach with detailed applications to the corresponding smooth multivariate Gauss–Weierstrass singular integral operators. The results are quantitative via Jackson-type inequalities involving the first uniform and L p moduli of continuity.

Suggested Citation

  • George A. Anastassiou, 2023. "Trigonometric Induced Multivariate Smooth Gauss–Weierstrass Singular Integrals Approximation," Mathematics, MDPI, vol. 12(1), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:115-:d:1309679
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