An Integral for Cesàro Summable Series
Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 85-97

Voir la notice de l'article provenant de la source Cambridge University Press

The pk+2 - integral of James [2] is strong enough to integrate a trigonometric series of the form 1.1 which is summable (C, k) in [0,2π], provided an extra condition holds involving the conjugate series 1.2 Considering series with coefficients o(n), Taylor [5] constructed an integral (the AP-integral) which successfully integrates series of the form (1. 1) which are Abel summable provided an extra condition holds involving the Abel means of the conjugate series (1.2).
Cross, George. An Integral for Cesàro Summable Series. Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 85-97. doi: 10.4153/CMB-1967-010-1
@article{10_4153_CMB_1967_010_1,
     author = {Cross, George},
     title = {An {Integral} for {Ces\`aro} {Summable} {Series}},
     journal = {Canadian mathematical bulletin},
     pages = {85--97},
     year = {1967},
     volume = {10},
     number = {1},
     doi = {10.4153/CMB-1967-010-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-010-1/}
}
TY  - JOUR
AU  - Cross, George
TI  - An Integral for Cesàro Summable Series
JO  - Canadian mathematical bulletin
PY  - 1967
SP  - 85
EP  - 97
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-010-1/
DO  - 10.4153/CMB-1967-010-1
ID  - 10_4153_CMB_1967_010_1
ER  - 
%0 Journal Article
%A Cross, George
%T An Integral for Cesàro Summable Series
%J Canadian mathematical bulletin
%D 1967
%P 85-97
%V 10
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-010-1/
%R 10.4153/CMB-1967-010-1
%F 10_4153_CMB_1967_010_1

[1] 1. Hardy, G. H., Divergent Series. Oxford (1944). Google Scholar

[2] 2. James, R. D., Generalized nth Primitives. Trans. Amer. Math. Soc. vol. 76 (1955), pages 149-176. Google Scholar

[3] 3. James, R. D., Summable Trigonometric Series. Pacific J. Math. 6 (1955), pages 99-110. Google Scholar

[4] 4. Jeffery, R. L., Trigonometric Series. Toronto (1955). Google Scholar

[5] 5. Taylor, S. J., An Integral of Perron ‘ s Type. Quart. J.Math. Oxford (2). vol. 6 (1955), pages 255-274. Google Scholar

[6] 6. Verblunsky, S., On the Theory of Trigonometric Series II. Proc. London Math. Soc. 34(1933), pages 457-491. Google Scholar

[7] 7. Verblunsky, S., On the Theory of Trigonometric Series VI. Proc. London Math. Soc. 38 (1933), pages 284-326. Google Scholar

[8] 8. Zygmund, A., Trigonometric Series. (2nd è d., Cambridge, 1958) I. Google Scholar

[9] 9. Zygmund, A., Trigonometric Series. (2nd èd., Cambridge, 1958) II. Google Scholar

Cité par Sources :