Convexity theorems for Fourier series

Kenji YANO

doi:10.2969/jmsj/01420119

Kenji YANO

著者情報

ジャーナルフリー

1962 年 14 巻 2 号 p. 119-149

DOI https://doi.org/10.2969/jmsj/01420119

詳細

Published: 1962 Received: 1959/03/16 Available on J-STAGE: 2006/09/26 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/26 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. Riesz, Sur un théorème de la moyenne et ses application, Acta Szeged, 1 (1922), 114-126.
2) A. L. Dixson and W. L. Ferrar, On Cesàro sums, J. London Math. Soc., 7 (1932), 87-93.
3) M. N. Obrechkoff, Sur la sommation des séries trigonométriques de Fourier par les moyennes arithmétiques, Bull. Soc. Math. France, 62 (1934), 84-109.
4) L. S. Bosanquet, A mean value theorem, J. London Math. Soc., 16 (1941), 146-148.
5) L. S. Bosanquet, Note on convexity theorems, J. London Math. Soc., 18 (1943), 239-248.
6) F. T. Wang, A note on Cesàro summability of Fourier series, Ann. of Math. (2), 44 (1943), 379-400.
7) J. M. Hyslop, Note on group of theorems in the theory of Fourier series, J. London Math. Soc., 24 (1949), 91-100.
8) S. Izumi, Notes on Fourier analysis (XXVII): A theorem on Cesàro summation, Tohoku Math. J. (2), 3 (1951), 212-215.
9) G. Sunouchi, Notes on Fourier analysis (XLVII): Convexity theorems and Cesàro summability of Fourier series, J. Math., Tokyo Metropolitan Univ., 1 (1953), 104-109.
10) K. Kanno, On the Cesàro summability of Fourier series (II), Tohoku Math. J. (2), 7 (1955), 265-278.
11) K. Yano, On a method of Cesàro summation for Fourier series, Kodai Math. Semi. Rep., 9 (1957), 49-58.
12) K. Yano, Notes on Tauberian theorems for Riemann summability, Tohoku Math. J. (2), 10 (1958), 19-31.
13) K. Yano, On convergence criteria for Fourier series II, Tohoku Math. J. (2), 11 (1959), 54-62.
14) K. Yano, On Fejér kernels, Proc. Japan Acad., 35 (1959), 59-64.
15) K. Yano, Some notes on Cesàro summation, Proc. Japan Acad., 35 (1959), 578-583.
16) A. Zygmund, Trigonometrical series, Warszawa-Lwow, 1935.
17) E. W. Hobson, The theory of functions of a real variable II, 1936, Cambridge.

Right : [1] M. Riesz, Sur un théorème de la moyenne et ses application, Acta Szeged, 1 (1922), 114-126.
[2] A. L. Dixson and W. L. Ferrar, On Cesàro sums, J. London Math. Soc., 7 (1932), 87-93.
[3] M. N. Obrechkoff, Sur la sommation des séries trigonométriques de Fourier par les moyennes arithmétiques, Bull. Soc. Math. France, 62 (1934), 84-109.
[4] L. S. Bosanquet, A mean value theorem, J. London Math. Soc., 16 (1941), 146-148.
[5] L. S. Bosanquet, Note on convexity theorems, J. London Math. Soc., 18 (1943), 239-248.
[6] F. T. Wang, A note on Cesàro summability of Fourier series, Ann. of Math. (2), 44 (1943), 379-400.
[7] J. M. Hyslop, Note on group of theorems in the theory of Fourier series, J. London Math. Soc., 24 (1949), 91-100.
[8] S. Izumi, Notes on Fourier analysis (XXVII): A theorem on Cesàro summation, Tôhoku Math. J. (2), 3 (1951), 212-215.
[9] G. Sunouchi, Notes on Fourier analysis (XLVII): Convexity theorems and Cesàro summability of Fourier series, J. Math., Tôkyo Metropolitan Univ., 1 (1953), 104-109.
[10] K. Kanno, On the Cesàro summability of Fourier series (II), Tôhoku Math. J. (2), 7 (1955), 265-278.
[11] K. Yano, On a method of Cesàro summation for Fourier series, Kôdai Math. Semi. Rep., 9 (1957), 49-58.
[12] K. Yano, Notes on Tauberian theorems for Riemann summability, Tôhoku Math. J. (2), 10 (1958), 19-31.
[13] K. Yano, On convergence criteria for Fourier series II, Tôhoku Math. J. (2), 11 (1959), 54-62.
[14] K. Yano, On Fejér kernels, Proc. Japan Acad., 35 (1959), 59-64.
[15] K. Yano, Some notes on Cesàro summation, Proc. Japan Acad., 35 (1959), 578-583.
[16] A. Zygmund, Trigonometrical series, Warszawa-Lwow, 1935.
[17] E. W. Hobson, The theory of functions of a real variable II, 1936, Cambridge.

訂正日: 2006/09/26 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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