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On functional Nörlund methods

Published online by Cambridge University Press:  24 October 2008

B. Choudhary
B. Choudhary
Affiliation:
I.I.T. Delhi, Haus-Khas, New Delhi 29, India
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Extract

Integral transformations analogous to the Nörlund means have been introduced and investigated by Kuttner, Knopp and Vanderburg(6), (5), (4). It is known that with any regular Nörlund mean (N, p) there is associated a function

regular for |z| < 1, and if we have two Nörlund means (N, p) and (N, r), where (N, pr is regular, while the function is regular for |z| ≤ 1 and different) from zero at z = 1, then q(z) = r(z)p(z) belongs to a regular Nörlund mean (N, q). Concerning Nörlund means Peyerimhoff(7) and Miesner (3) have recently obtained the relation between the convergence fields of the Nörlund means (N, p) and (N, r) on the one hand and the convergence field of the Nörlund mean (N, q) on the other hand.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 1 , January 1970 , pp. 47 - 60
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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