References
Chandrasekharan, K., andS. Minakshisundaram: Typical Means. Oxford 1952.
Hardy, G. H.: Divergent Series. Oxford 1949.
Hardy, G. H., andM. Riesz: The General Theory of Dirichlet's Series. Cambridge 1915.
Hyslop, J. M.: The absolute summability of series by Rieszian means. Proc. Edinburgh Math. Soc. (2)5, 46–54 (1936).
Hyslop, J. M.: A Tauberian theorem for absolute summability. J. London Math. Soc.12, 176–180 (1937).
Landau, E.: Über die Konvergenz einiger Klassen von unendlichen Reihen am Rande des Konvergenzgebietes. Monatshefte für Math.18, 8–28 (1907).
Lorentz, G. G., andM. S. Macphail: Direct theorems on methods of summability. III: Absolute summability functions. Math. Z.59, 375–386 (1953/54).
Obrechkoff, N.: Sur la sommation absolute des séries de Dirichlet. C. R. Acad. Sci. Paris186, 215–217 (1928).
Obrechkoff, N.: Über die absolute Summierung der Dirichletschen Reihen. Math. Z.30, 375–386 (1929).
Rajagopal, C. T.: On Riesz summability and summability by Dirichlet's series. Amer. J. Math.69, 371–378, 851 –852 (1947).
Schnee, W.: Über Dirichletschen Reihen. Rendiconti di Palermo27, 87–116 (1909).
Tauber, A.: Ein Satz aus der Theorie der unendlichen Reihen. Monatshefte für Math.8, 273–277 (1897).
Widder, D. V.: The Laplace Transform. Princeton 1941.
Zygmund, A.: On certain integrals. Trans. Amer. Math. Soc.55, 170–194 (1944).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Srivastava, P. Tauberian theorems for absolute summability of series and integrals. Math Z 73, 460–465 (1960). https://doi.org/10.1007/BF01215518
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01215518