Inclusion Theorems for the Absolute Summability of Divergent Integrals
Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 389-398

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

Some inclusion theorems are obtained relating the absolute summability of divergent integrals of the form under three summability methods: Abelian A(x), Abelian A(lnx) and Stieltjes S(x).
DOI : 10.4153/CMB-1983-065-7
Mots-clés : 40F05, 40D25, 40G99
Diamond, Harvey; Kuttner, Brian; Raphael, Louise A. Inclusion Theorems for the Absolute Summability of Divergent Integrals. Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 389-398. doi: 10.4153/CMB-1983-065-7
@article{10_4153_CMB_1983_065_7,
     author = {Diamond, Harvey and Kuttner, Brian and Raphael, Louise A.},
     title = {Inclusion {Theorems} for the {Absolute} {Summability} of {Divergent} {Integrals}},
     journal = {Canadian mathematical bulletin},
     pages = {389--398},
     year = {1983},
     volume = {26},
     number = {4},
     doi = {10.4153/CMB-1983-065-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-065-7/}
}
TY  - JOUR
AU  - Diamond, Harvey
AU  - Kuttner, Brian
AU  - Raphael, Louise A.
TI  - Inclusion Theorems for the Absolute Summability of Divergent Integrals
JO  - Canadian mathematical bulletin
PY  - 1983
SP  - 389
EP  - 398
VL  - 26
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-065-7/
DO  - 10.4153/CMB-1983-065-7
ID  - 10_4153_CMB_1983_065_7
ER  - 
%0 Journal Article
%A Diamond, Harvey
%A Kuttner, Brian
%A Raphael, Louise A.
%T Inclusion Theorems for the Absolute Summability of Divergent Integrals
%J Canadian mathematical bulletin
%D 1983
%P 389-398
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-065-7/
%R 10.4153/CMB-1983-065-7
%F 10_4153_CMB_1983_065_7

[1] 1. Erdelyi, A., Magnus, W., Oberkettinger, F., Tricomi, F. G., Tables of Integral Transforms, Vol. 2 (McGraw Hill, 1954). Google Scholar

[2] 2. Hardy, G. H., Divergent Series (Oxford 1949) pp. 73 ff. Google Scholar

[3] 3. Knopp, K., Norlund Method for Functions, Math Z, 63 (1955), pp. 39-52. Google Scholar

[4] 4. Paley, R. E. A. C. and Wiener, N., Fourier Transforms in the Complex Domain (AMS 1934) pp. 8 ff. Google Scholar

[5] 5. Raphael, L. A., The Stieltjes Summability Method and Summing Sturm-Liouville Expansions, SI AM Journal on Mathematical Analysis, 13 (1982), pp. 676-689. Google Scholar

[6] 6. Rath, D., An Inclusion Theorem on Summability, J. London Math Soc. (2), 16 (1977), pp. 493-489. Google Scholar

[7] 7. Tikhonov, A. N., Stable Methods for the Summation of Fourier Series, Soviet Math. Dokl. 5 (1964), pp. 641-644. Google Scholar

[8] 8. Graffi, S., Stieltjes Summability and Convergence of the Fade Approximants for the Vacuum Polarization by an External Field, J. Math. Phys., 14 (1973), pp. 1184-1186. Google Scholar

Cité par Sources :