푸리에 급수에 대한 체사로 총합가능성의 고전적 결과에 관하여
On the classical results of Cesàro summability for Fourier serie
0
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
체사로 총합가능성(Cesàro summability)은 푸리에 급수(Fourier series)의 삼각계 급수가 어떤 의미로 주어진 본래 함수를 표현하느냐를 논하는데 효과적인 수렴성을 가지고 있다.따라서 본 논문에서는 1897년 부터 1950년 말까지 푸리에 급수 등의 총합가능성에 대한 고전적인 결과들을 고찰하고 특히 이들 중에서 푸리에 급수에 대한 체사로 총합가능성에 관한 연구들 중 주목되는 연구결과들을 중심으로 연구 소계보를 제시한다.
Abstract
This paper is concerned with the Cesàro summability of Fourier series. Many authors have studied on the summability of Fourier series up to now. Also, G. H. Hardy and J. E. Littlewood \cite{b3}, Gaylord M. Merriman \cite{b4}, L. S. Bosanquet \cite{b14}, Fu Traing Wang \cite{b15} and others had studied the Cesàro summability of Fourier series until the first half of the 20th century. In the section 2, we reintroduce Ernesto Cesàro's life and the meaning of mathematical history for Cesàro's work. In the section 3, we investigate the classical results of summability for Fourier series from 1897 to the mid-twentieth century. In conclusion, we restate the important classical results of several theorems of Cesàro summability for Fourier series. Also, we present the research minor lineage of Cesàro summability for Fourier series.
참고문헌 (29)
- L. S. Bosanquet, "A solution of the Cesàro summability problem for successively derived Fourier series", Proc. London Math. Soc, 2(46), pp.270~289 (1940)
- Kien Kwong Chen, "On the Absolute Cesàro Summability of Negative Order for a Fourier Series at a Given Point", American Journal of Mathematics, 66(2), pp.299~312 (1944)
- Lipót Fejér, "Sur les functions bornée set intêgrables", C. R. Acad. Sci. Paris, 131, pp.984~987 (1900)
- John J. Gergen, "Convergence and summability criteria for Fourier series", Quarterly Journal of Mathematics, 1, pp.252~275 (1930)
- G. H. Hardy, "Solution of the Cesàro summability problem for power series and Fourier series", Mathematische Zeitschrift, 19, pp.67~96 (1924)
- Einar Hille, "On the summability of Fourier series", Proc. N. A. S, 14 (1928)
- Einar Hille, "On the Summability of Fourier Series I", Transactions of the Amer. Math. Soc, 34, pp.757~783 (1932)
- Einar Hille, "On the Summability of Fourier Series II", Annals of Mathematics Second Series, 34(2), pp.329~348 (1933)
- Einar Hille, "On the Summability of Fourier Series II", Annals of Mathematics Second Series, 34(3), pp.602~605 (1933)
- Kosi Kanno, "On The Cesàro summability of Fourier series (II)", Tohoku Mathematical Journal Second Series, 7(3), pp.265~278 (1955)
- Masakiti Kinukawa, "On The Cesàro summability of Fourier series I", Tohoku Math. Journal, 6(2–3), pp.109~120 (1954)
- Masakiti Kinukawa, "On The Cesàro summability of Fourier series II", Tohoku Math. Journal Second Series, 7(3), pp.252~264 (1955)
- Sulaxana Kumari, "On the order of the Cesàro means of Fourier series and its successively derived series", Proceedings: Physical sciences Part A, 23(3), pp.199~216 (1957)
- 이정오, "푸리에 일생, 푸리에 후학의 소계보와 L1-수렴성에 관한 테라코브스키의 정리", 한국수학사학회지, 22(1), pp.25~40 (2009), 한국수학사학회
- 이정오, "바티의 L1-수렴성 연구에 관한 소고", 한국수학사학회지, 27(1), pp.81~93 (2014), 한국수학사학회[DOI]
- 이정오, "이중 푸리에 급수의 총합가능성과 수렴성에 대한 고전적인 연구들에 관하여", 한국수학사학회지, 27(4), pp.285~297 (2014), 한국수학사학회[DOI]
- 이정오, "Lp(T2)-수렴성과 모리츠에 관하여", 한국수학사학회지, 28(6), pp.321~332 (2015), 한국수학사학회[DOI]
- Gaylord M. Merriman, "A Set of Necessary and Sufficient Conditions for the Cesàro Summability of Double Series", Annals of Mathematics Second Series, 29(1, pp.4) (1927), 343~354
- Niels Erik Nørlund, "Sur une application des fonctions permutables", Lunds Universitets Arsskrift N. F., 16(2), pp.3~10 (1919)
- Alfredo Perna, "Ricordo di Ernesto Cesàro (1859–1906)", Bollettino dell’Unione MatematLee ica Italiana, 11(3), pp.457~468 (1956)
- B. N. Prasad, "The Absolute Summability (A) of Fourier Series", pp.1930
- W. C. Randels, "On the summability of Fourier series", Transactions of the Amer. Math. Soc, 41(1), pp.24~47 (1937)
- Gen Ichiro Sunouchi, "Cesàro Summability of Fourierseries", Tohoku Mathematical Journal Second Series, 5(2), pp.198~210 (1953)
- Fu Traing Wang, "A Note on Cesàro Summability of Fourier Series", Annals of Mathematics Second Series, 44(3), pp.397~400 (1943)
- J. M. Whittaker, "The absolute summability of Fourier series", Proc. Edinburgh Math. Soc, 2, pp.1~5 (1930)
- Kenji Yano, "On a method of Cesàro summation for Fourier series", Kodal mathematical seminar reports, 9(2), pp.49~58 (1957)
- Shigeki Yano, "Note on Fourier analysis. XXXI. Cesàro summability of Fourier series", Pacific J. Math, 2(3), pp.419~429 (1952)
- Shigeki Yano, "Cesàro Summability of Fourier series", Tohoku Mathematical Journal Second Series, 5(2), pp.196~197 (1953)
- William Henry Young, "On classes of summable functions and their Fourier series", Proceedings of the Royal Society of London Series A, pp.225~229 (1912)