TY - JOUR
AU - Rajagopal, C. T.
AB - 242 S. MINAKSHISUNDARAM and C. T. RAJAOOPAL [25 Jan. AN EXTENSION OF A TAUBERIAN THEOREM OF L. J. MORDELL By S. MINAKSHISUNDARAM and C. T. RAJAGOPAL [Received 3 December 1944—Read 25 January 1945] 1. This paper seeks to extend a Tauberian theorem of L. J . Mordell involving the first-order Cesaro mean (9)* by substituting for the Cesaro a Riesz mean of any order r > 0. Three points regarding the extension mean may be mentioned at the outset, (i) The particular case r = 1 of the exten- sion seems t o be superior to a similar extension by N. Higaki (5, theorem IV), in tha t it serves t o amplify the familiar Hardy-Landau convergence theorem for series summable by the first Riesz mean (6, 31 f.). (ii) The general case r > 0 of our extension shows how one of K. Ananda Rau's theorems on series (1, theorem 4 and 8, theorem 1; also 2, theorem 2) may be restated with a one-sided restriction on the terms of the series instead of his two-sided restriction, (iii) The case r > 1 of the extension is proved by a method which H. D. Kloosterman(7) suggests for obtaining 
TI - An Extension of a Tauberian Theorem of L. J. Mordell
JO - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s2-50.4.242
DA - 1948-01-01
UR - https://www.deepdyve.com/lp/wiley/an-extension-of-a-tauberian-theorem-of-l-j-mordell-FHlNNn00hB
SP - 242
EP - 255
VL - s2-50
IS - 1
DP - DeepDyve
ER -