한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
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푸리에 일생, 푸리에 후학의 소계보와 $L^1$-수렴성에 관한 테라코브스키의 정리

The Life of Fourier, The minor Lineage of His Younger Scholars and a Theorem of Telyakovskii on $L^1$-Convergence

  • Lee, Jung-Oh (Department of Mathematics, ChoSun University)
  • 발행 : 2009.02.28
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⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 푸리에의 생애와 18세기 말 그의 스승과 19세기부터 20세기까지는 그의 제자와 후학들의 소계보를 살펴보고 특히, 비교적 덜 접근된 러시아 수학자들의 푸리에 급수의 $L^1$-수렴성에 대한 연구결과들 중 푸리에 계수 성질을 이용한 푸리에 급수 수렴성에 대해 매우 의미 있는 연구를 이룩한 콜모고로프, 테라코브스키의 연구결과에 관심을 갖고 이들의 연구 결과를 비교하여 조사하였다.

This study concerns with John B. Fourier' s life, his teachers, his younger scholars and the $L^1$-convergence of Fourier series. First, we introduce the correlation between the French Revolution and Fourier who is significant in the history of mathematics. Second, we investigate Fourier' s teachers, students and a minor lineage of his younger scholars from 19th century to 20th century. Finally, we compare the theorem of Telyakovskii with the theorem of kolmogorov on $L^1$-convergence of Fourier series.

키워드

참고문헌

  1. Mathematics Genealogy Project Department of Mathematics, North Dakota State University, 2008.
  2. I Grattan-Guinness, J R Ravetz, Biography in Dictionary of Scientific Biography, New York, 1970-1990.
  3. Biography in Encyclopaedia Britannica [Available on the web].
  4. Wikipedia Encyclopedia [Available on the web].
  5. http:;/www-gap.dcs.st-and.ac.uk/nistorylBiographies/Fourier.html
  6. J Herivel, Joseph Fourier. The Man and the Physicist, Oxford, 1975.
  7. 한국과학기술정보연구원, 푸리에 급수, 사이언스 21 No. 119, 2006.
  8. F Arago, Joseph Fourier, Biographies of Distinguished Scientific Men, London (1957), 242-286.
  9. S Bochner, Fourier series came first, Amer. Math. Monthly 86(1979), No.3, 197-199. https://doi.org/10.2307/2321520
  10. A C Bose, Fourier, his life and work, Bulletin of the Calcutta Mathematical Society 7 (1916), 33-48.
  11. L Charbonneau, Fourier l'homme et le physicien d'apres John Herivel, Rev. Histoire Sci. Appl. 29(1976), No.1 63-72. https://doi.org/10.3406/rhs.1976.1374
  12. W A Coppel, J B, Fourier-on the occasion of his two hundredth birthday, Amer. Math. Monthly 76 (1969), 468-483. https://doi.org/10.2307/2316953
  13. A Dahan-Dalmedico, Realite physique et objets mathematiques chez Fourier, in Faire de l'histoire des mathematiques : documents de travail (Paris,1987), 1-255.
  14. I Grattan-Guinness, Joseph Fourier and the revolution in mathematical physics, Journal of the Institute of Mathematics and its Applications 5(1969), 230-253. https://doi.org/10.1093/imamat/5.2.230
  15. J Langins, Une lettre inedite de Fourier sur l'enseignement destine awe ingenieursen 1797, Rev. Histoire Sci. Appl. 34(3-4) (1981), 193-207. https://doi.org/10.3406/rhs.1981.1765
  16. V A Nikiforovskii, Mathematician, statesman, citizen (on the 225th anniversary of the birth of Jean Baptiste Joseph Fourier) (Russian), Vestnik Ross. Akad. Nauk 63(8) (1993), 743-746.
  17. F S Shoucair, Joseph Fourier's analytical theory of heat: a legacy to science and engineering, IEEE transactions on education 32 (1989), 359-366. https://doi.org/10.1109/TE.1989.386497
  18. S Takata, J B Fourier in the history of thermal radiation research, Historia Sci. 2(3) (1993), 203-221.
  19. H Yoshida and S Takata, The growth of Fourier's theory of heat conduction and his experimental study, Historia Sci. 1(1) (1991), 1-26.
  20. A. N. Kolmogorov, Sur I'ordre de grandeur des coefficients de la serie de Fourier- Lebesgue, Bull. Internat. Acad. Polon. Sci. (1923), 83-86.
  21. S. A. Telyakovskii, Concerning a sufficient condition of Sidon for the integrability of trigonometric series, Math, Notes 14 (1973), 742-748. https://doi.org/10.1007/BF01147448
  22. S. A. Telyakovskii Mat. Zametki, 72(6) (2002), 949 - 953. https://doi.org/10.4213/mzm677
  23. A. S. Belov, S. A. Telyakovskii, Mat. Sb., 198(6) (2007), 25 - 40. https://doi.org/10.4213/sm2420
  24. 장승준, 함수공간에서의 일반화된 푸리에-파인만 변환에 관한 고찰, 한국수학사학회지, 20(2007), No. 3, 73-90,
  25. 김화준, 유계변동과 관련된 Waterman의 연구에 대하여, 한국수학사학회지, 19(2006), No. 2 115-124