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Stanojevic의 푸리에 급수의 $\mathfrak{L}^1$-수렴성 연구의 소 계보 고찰

A Brief Study on Stanojevic's Works on the $\mathfrak{L}^1$-Convergence

  • Lee, Jung Oh (Department of Mathematics, ChoSun University)
  • 투고 : 2013.01.20
  • 심사 : 2013.03.25
  • 발행 : 2013.05.31

초록

본 논문은 저자의 선행 연구 결과에 따른 부가적인 연구로 '푸리에 급수의 $\mathfrak{L}^1$-수렴성'에 관한 많은 업적을 남긴 세계적인 수학자인 스타노제빅(Caslav V. Stanojevic)을 중심으로 20세기 후반부터 21세기 초까지(1973-2002) 30년간 그의 연구결과를 순차적으로 고찰하여 푸리에 급수의 $\mathfrak{L}^1$-수렴성 연구자들의 2012년까지 소 계보를 조사한다.

This study concerns Stanojevic's academic works on the $\mathfrak{L}^1$-convergence of Fourier series from 1973 to 2002. We review his academic works. Also, we briefly investigate a simple academic lineage for the researchers of $\mathfrak{L}^1$-convergence of Fourier series until 2012. First, we introduce the classical lineage of the researchers for $\mathfrak{L}^1$-convergence Fourier series in section 2. Second, we investigate the backgrounds of Stanojevic's study at Belgrade University and University of Missouri-Rolla respectively. Finally, we compare and consider the $\mathfrak{L}^1$-convergence theorems of Stanojevic's results from 1973 to 2002 successively. In addition, we compose a the simple lineage of $\mathfrak{L}^1$-convergence of Fourier series from 1973 to 2012.

키워드

참고문헌

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  11. John. W. Garrett and Caslav. V. Stanojevic,"On $L^1$-convergence of certain cosine sums", Proc. Amer. Math. Soc., 54(1976), 101-105.
  12. John.W. Garrett and Caslav. V. Stanojevic", Necessary and sufficient conditions for$L^1$- convergence of trigonometric series", Proc. Amer. Math. Soc., 60(1976), 68-74.
  13. John W. Garrett, C.S. Rees and Caslav V. Stanojevic,"On $L^1$-convergence of Fourier series with quasi-monotone coefficients", Proc. Amer. Math. Soc., 72(1978), 535-538.
  14. John W. Garrett, C. S. Rees and Caslav V. Stanojevic"$L^1$-convergence of Fourier series with coefficients of bounded variation", Proc. Amer. Math. Soc., 80(3) (1980), 423-430. https://doi.org/10.1090/S0002-9939-1980-0580997-7
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  16. Kulwinder Kaur and S.S. Bhatia,"Integrability and $L^1$-convergence of Rees-Stanojevic sums with generalized semi-convex coefficients", IJMMS, 30(11) (2002), 645-650.
  17. Kulwinder Kaur,"Integrability and $L^1$-convergence of Rees-Stanojevic sums with generalized semi-convex coefficients of non-integral orders", Archivum Mathematicum (brno) Tomus, 41(2005) 423-437.
  18. Laszlo Leindler,"On $L^1$-convergence of sine series", Analysis Mathematica, 38(2) (2012), 123-133. https://doi.org/10.1007/s10476-012-0203-7
  19. Karanvir Singh and Kulwinder Kaur,"On the $L^1$-convergence of certain generalized modified trigonometric sums", Matematiqki Vesik, 61(3) (2009), 219-226.
  20. Caslav V. Stanojevic,"Classes of $L^1$-convergence of Fourier-Stieltjes series", Proc. Amer. Math. Soc., 82(2) (1981), 209-215. https://doi.org/10.1090/S0002-9939-1981-0609653-4
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  22. Caslav V. Stanojevic,"O-regularly varying convergence moduli of Fourier and Fourier- Stieltjes series", Math. Ann., 279(1987), 103-115. https://doi.org/10.1007/BF01456193
  23. Caslav V. Stanojevic,"Structure of Fourier and Fourier-Stieltjes coefficients of series with slowly varying convergence moduli", Bull. Amer. Math. Soc.,19(1) (1988).
  24. Caslav V. Stanojevic,"The Fourier character of series with slowly varying convergence moduli", Publications de L'institut Mathematique, 48(62) (1990), 91-95.
  25. Caslav V. Stanojevic and Vera B. Stanojevic,"Tauberian retrieval theory", Publications de l'Institut Mathematique, 71(85) (2002), 105-111. https://doi.org/10.2298/PIM0271105S
  26. Vera B. Stanojevic,"$L^1$-Convergence of Fourier Series with Complex Quasimonotone Coefficients", Proc. Amer. Math. Soc., 86(2) (1982), 241-247. https://doi.org/10.1090/S0002-9939-1982-0667282-1
  27. Charles S. Rees and Caslav V. Stanojevic,"Necessary and sufficient conditions for integrability of certain cosine sums", Journal of Mathematical Analysis and Applications, 43(1973), 579-586. https://doi.org/10.1016/0022-247X(73)90278-3

피인용 문헌

  1. On Classical Studies for Summability and Convergence of Double Fourier Series vol.27, pp.4, 2014, https://doi.org/10.14477/jhm.2014.27.4.285
  2. A Brief Study on Bhatia's Research of L1-Convergence vol.27, pp.1, 2014, https://doi.org/10.14477/jhm.2014.27.1.081