Convergence Factors for Double Series Summable by Nörlund Means.
نویسنده
چکیده
In a note' published in volume 21 of these PROCEEDINGS I gave necessary and sufficient conditions for convergence factors in simply infinite series summable by N6rlund means. The purpose of the present note is to furnish analogous results for double series. We are given a doubly infinite set of complex constants cij (i, j = 0, 1, 2, 3, .. .), where coo 0 0 and Zc,ix'y' is convergent for I x I < 1, I y I < 1, and becomes infinite as (x, y) approaches (1, 1) through real values. We set m n
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ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 22 3 شماره
صفحات -
تاریخ انتشار 1936