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The Complete Asymptotic Evaluation for General Modified Mellin–Gauss–Weierstrass Convolution Operators

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Abstract

We use the results from the very recent paper (Popa in Constr Approx, 2022. https://doi.org/10.1007/s00365-022-09584-3) to prove the complete asymptotic evaluation for general modified Mellin–Gauss–Weierstrass convolution operators.

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References

  1. Aral, A., Erbay, H., Yılmaz, B.: On modified Mellin–Gauss–Weierstrass convolution operators. Results Math. 77(3), 1 (2022). (Paper No. 130, p 18)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bardaro, C., Mantellini, I.: Voronovskaya-type estimate for Mellin convolution operators. Results Math. 50(1–2), 1–16 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bardaro, C., Mantellini, I.: A note on the Voronovskaja theorem for Mellin–Fejer convolution operators. Appl. Math. Lett. 24(12), 2064–2067 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bardaro, C., Mantellini, I.: On Mellin convolution operators: a direct approach to the asymptotic formulae. Integral Transforms Spec. Funct. 25(3), 182–195 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Butzer, P.L., Jansche, S.: A direct approach to the Mellin transform. J. Fourier Anal. Appl. 3, 325–375 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Butzer, P.L., Nessel, R.J.: Fourier Analysis and Approximation I. Academic Press, New York (1971)

    Book  MATH  Google Scholar 

  7. Kolbe, W., Nessel, R.J.: Saturation theory in connection with Mellin transform methods. SIAM J. Math Anal. 1972(3), 246–262 (2021)

    MathSciNet  MATH  Google Scholar 

  8. Popa, D.: The complete asymptotic evaluation for Mellin convolution operators. Constr. Approx. (2022). https://doi.org/10.1007/s00365-022-09584-3

    Article  MATH  Google Scholar 

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Acknowledgements

We would like to express our gratitude to the two reviewers for their very careful reading of the manuscript and many valuable and constructive comments that have improved the final version of the paper.

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The author declare that no funds, grants, or other support were received during the preparation of this manuscript.

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  1. Department of Mathematics, Ovidius University of Constanţa, Bd. Mamaia 124, 900527, Constanţa, Romania

    Dumitru Popa

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  1. Dumitru Popa
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Correspondence to Dumitru Popa.

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Popa, D. The Complete Asymptotic Evaluation for General Modified Mellin–Gauss–Weierstrass Convolution Operators. Results Math 78, 36 (2023). https://doi.org/10.1007/s00025-022-01815-0

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  • DOI: https://doi.org/10.1007/s00025-022-01815-0

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