푸리에 급수에 대한 총합가능성의 결과들에 관하여
On the Results of Summability for Fourier series
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
체사로 총합가능성(Cesàro summability)은 무한급수에 대한 일반화된 수렴 판단 도구 중 하나이다. 본 논문에서는 1897년부터 1957년까지 고전적인 결과들에 이어 1960년부터 2010년까지 푸리에 급수 등의 총합가능성에 대한 몇가지 결과들을 순차적으로 고찰한다. 특히, 1960년부터 1989년까지 푸리에 급수의 총합가능성에 관한 신고전적인 연구 결과들은 피터슨(G.M. Petersen), 코시켄노(Kôsi Kanno), 시나(S.R. Sinha), 푸청셍(Fu Cheng Hsiang), 프렘 찬드라(Prem Chandra), 딕싯(G. D. Dikshit), 로어드스(B. E. Rhoades) 등에 의하여 주도 되었다. 결론에서 보어(Hüseyin Bor)의 연구 중 $|\bar{ N}, p_n |_k-$ 총합가능성과 $ |\bar{ N} , p_n , \gamma |_k -$ 총합가능성 등을 살펴보고 1960년부터 2010년까지 푸리에 급수의 총합가능성에 관한 연구 소 계보를 제시한다. }
Abstract
Cesàro summability is a generalized convergence criterion for infinite series. We have investigated the classical results of summability for Fourier series from 1897 to 1957. In this paper, we are concerned with the summability and summation methods for Fourier Series from 1960 to 2010. Many authors have studied the subject during this period. Especially, G.M. Petersen, Kôsi Kanno, S.R. Sinha, Fu Cheng Hsiang, Prem Chandra, G. D. Dikshit, B. E. Rhoades and others had studied neoclassical results on the summability of Fourier series from 1960 to 1989. We investigate the results on the summability for Fourier series from 1990 to 2010 in section 3. In conclusion, we present the research minor lineage on summability for Fourier series from 1960 to 2010. Hüseyin Bor is the earliest researcher on $ | \bar{ N}, p_n |_k$- summability. Thus we consider his research results and achievements on $ | \bar{ N}, p_n |_k$- summability and $ |\bar{ N} , p_n , \gamma |_k$- summability.
참고문헌 (38)
- E. S. Belinskii, "Strong summability of Fourier series of the periodic functions from Hp(0 < p ≤ 1)", Constructive Approximation, 12(2), pp.187~195 (1996)
- Hüseyin Bor, "Absolute Norlund summability factors of power series and Fourier series", Ann. Polon. Math, 56, pp.11~17 (1991)
- Hüseyin Bor, "A note on local property of factored Fourier series", Nonlinear Analysis Theory Methods & Applications, 64(3), pp.513~517 (2006)
- Hüseyin Bor, "A study on local properties of Fourier series", Nonlinear Analysis: Theory, Methods & Applications, 57(2), pp.191~197 (2004)
- Hüseyin Bor, "Local properties of factored Fourier series", Applied Mathematics and Computation, 212(1), pp.82~85 (2009)
- Hüseyin Bor, "Local property of j |N ; pnjk summability of factored Fourier series", Bull. Inst. Math. Acad. Sinica, 17, pp.165~170 (1989)
- Hüseyin Bor, "On local property of j |N ; pn; δjk summability of factored Fourier series", Journal of mathematical analysis and applications, 179(2), pp.646~649 (1993)
- Hüseyin Bor, "On The Localization of Factored Fourier Series", Acta Universitatis Apulensis, 24, pp.239~245 (2010)
- Hüseyin Bor, "On the local property of j |N ; pnjk summability of factored Fourier series", J. Math. Anal. Appl, 163, pp.220~226 (1992)
- Prem Chandra, "On the jE; qj summability of a Fourier series and its conjugate series", Riv. Mar. Univ. Parma, 4(3), pp.65~78 (1977)
- Prem Chandra, "On the jBj and jE; qj summability of a fourier series its conjugate series and their derived series", Indian J. Pure appl. Math, 12(11), pp.1350~1360 (1981)
- H. P. Dikshit, "Absolute summability of Fourier series with factors", Pacific Journal of Mathematics, 61(1), pp.59~69 (1975)
- Ganesh D. Dikshit, "Absolute Riesz summability of Fourier series, II", Journal of mathematical analysis and applications, 102(2), pp.549~565 (1984)
- Hiroshi Hirokawa, "On the absolute Cesàro summability of Fourier series", Proceedings of the American Mathematical Society, 13(2), pp.236~243 (1962)
- Fu Cheng Hsiang, "On |C; 1| Summability Factors of Fourier series at a given point", Pacific Journal Math, 33(1), pp.139~147 (1970)
- Fu Cheng Hsiang, "On the Absolute Summability of a Fourier Series and its Conjugate Series", Proceedings of the American Mathematical Society, 11(1), pp.32~38 (1960)
- Kôsi Kanno, "on the absolute summability of fourier series (II)", Tohoku Mathematical Journal, 13(2), pp.201~215 (1961)
- Shyam Lal, "On almost(N; p; q)summability of conjugate Fourier series", International Journal of Mathematics and Mathematical Sciences, 25(6), pp.365~372 (2001)
- Shyam Lal, "On the study of conjugate series of a Fourier series by Kλ-summability methods", Tamkang Journal of Mathematics, 34(2), pp.147~154 (2003)
- 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]
- 이정오, "푸리에 급수에 대한 체사로 총합가능성의 고전적 결과에 관하여", 한국수학사학회지, 30(1), pp.17~29 (2017), 한국수학사학회[DOI]
- 이정오, "푸리에 일생, 푸리에 후학의 소계보와 L1-수렴성에 관한 테라코브스키의 정리", 한국수학사학회지, 22(1), pp.25~40 (2009), 한국수학사학회
- N. L. Pachulia, "On Strong Summability of Fourier Series of Summable Functions", Ukrainian Mathematical Journal, 52(8), pp.1264~1273 (2000)
- G. M. Petersen, "Summability of a class of Fourier series", Proceedings of the American Mathematical Society, 11(6), pp.994~998 (1960)
- A. Yu Petrovich, "On The Summability of generalized Fourier series by Abel’s method", Mathematics of the USSR-Sbornik, 50(1), pp.227~239 (1985)
- B. E. Rhoades, "Matrix summability of Fourier series based on inclusion theorems II", Journal of mathematical analysis and applications, 130(2), pp.525~537 (1988)
- Mehmet Ali Sarıgöl, "On local property of jAjk summability of factored Fourier series", Journal of mathematical analysis and applications, 188(1), pp.118~127 (1994)
- Mehmet Ali Sarıgöl, "On the local properties of factored Fourier series", Applied Mathematics and Computation, 216(11), pp.3386~3390 (2010)
- N. P. Schembari, "(C; 1)Summability of the Differentiated Fourier Series", Journal of Mathematical Analysis and Applications, 191(3), pp.633~646 (1995)
- S.R. Sinha, "A Theorem on the absolute Cesaro summability of fourier series", Proceedings of the National Institute of Sciences of India: Physical sciences, 29(1-3), pp.302~ (1963)
- W. T. Sulaiman, "On local property of j |N ; pn; δjk summability of factored Fourier series", Journal of mathematical analysis and applications, 292(2), pp.340~343 (2004)
- Gen-ichiro Sunouchi, "Some criteria for the absolute summability of a Fourier series", Tohoku Mathematical Journal, Second Series, 19(3), pp.311~314 (1967)
- István Szalay, "On the absolute summability of Fourier series", Tohoku Mathematical Journal Second Series, 21(4), pp.523~531 (1969)
- Antoni Zygmund, "Trigonometric series, Vol.1" (1959), Cambridge Univ.Press