Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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A Brief Study on Stanojevic's Works on the $\mathfrak{L}^1$-Convergence

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

  • Lee, Jung Oh (Department of Mathematics, ChoSun University)
  • Received : 2013.01.20
  • Accepted : 2013.03.25
  • Published : 2013.05.31
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Abstract

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.

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.

Keywords

References

  1. 이정오,"푸리에 일생, 푸리에 후학의 소계보와 $L^1$-수렴성에 관한 테라코브스키의 정리", 한국수학사학회지, 22(1) (2009), 25-40.
  2. 이정오,"푸리에 급수의 부분합, 푸리에 계수를 이용한 $L^1$-수렴성 결과들의 재해석과 그 소계보", 한국수학사학회지, 23(1) (2010), 53-66.
  3. 최원석 www.seoprise.com/board/ 서프라이즈 과학칼럼, 2007. 9. 27.
  4. 한국과학기술정보연구원,"푸리에 급수", 사이언스, 21(119) (2006).
  5. William O. Bray and Caslav V. Stanojevic", Tauberian$L^1$-convergence classes of Fourier series I", Trans. Amer. Math. Soc., 275(1) (1983), 59-69. https://doi.org/10.1090/S0002-9947-1983-0678336-3
  6. William O. Bray and Caslav V. Stanojevic", Tauberian$L^1$-convergence classes of Fourier series II", Math. Ann., 269(1984), 469-486. https://doi.org/10.1007/BF01450761
  7. Chang-Pao Chen and Yeu-Wen Chuang,"$L^1$-Convergence of Double Fourier Series", Taiwanese journal of mathematics, 19(4) (1991).
  8. F. J. Feng and S. P. Zhou,"On $L^1$-convergence of Fourier series of complex valued functions under the GM7 condition", Acta mathematica Hungarica, 133(1-2) (2011).
  9. John. W. Garrett and Caslav. V. Stanojevic,"On integrability and $L^1$-convergence of certain cosine sums", Notices Amer. Math. Soc., 7(8) (1975), 873-879.
  10. John. W. Garrett and Caslav. V. Stanojevic,"On $L^1$-convergence of certain cosine sums", Bull. Amer. Math. Soc., 82(1) (1976), 129-130. https://doi.org/10.1090/S0002-9904-1976-13990-0
  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
  15. David E. Grow and Caslav V. Stanojevic,"Convergence and the Fourier character of trigonometric transforms with slowly varying convergence moduli", Math. Ann., 302(1995), 433-472. https://doi.org/10.1007/BF01444502
  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
  21. Caslav V. Stanojevic", Tauberian conditions for$L^1$-convergence of Fourier series", Trans. Amer. Math. Soc., 271(1) (1982), 237-244. https://doi.org/10.1090/S0002-9947-1982-0648089-2
  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

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