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A Further Note on Lototsky-Type Transformations

Published online by Cambridge University Press:  20 November 2018

A. Meir
A. Meir*
Affiliation:
The University of Alberta, Calgary
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In two recent papers by V. F. Cowling and C. L. Miracle (1; 2), the regularity of generalized Lototsky transformations, as well as their application to the geometric series, has been investigated. The main interest of the papers centres around (1, Theorems 3.1 and 4.1) and (2, Theorem A). In (1, Theorem 3.1) and in (2, Theorem A), the authors stated and proved a set of sufficient conditions for the regularity of Lototsky-type transformations. In (1, Theorem 4.1), they proved under certain additional conditions that these transformations sum the geometric series ∑zn to (1 — z)–l if Re z < 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 221 - 224
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Cowling, V. F. and Miracle, C. L., Some results for the generalized Lctotsky transform, Can. J. Math., 14 (1962), 418–435.Google Scholar
2. Cowling, V. F. and Miracle, C. L., Corrections to and remarks on some results for the generalized Lototsky transform, Can. J. Math., 16 (1964), 423–428.Google Scholar
3. Jakimovski, A., A generalization cf the Lototsky method of summability, Mich. Math. J., 6 (1959), 277–290.Google Scholar
4. Meir, A., On the [F, dn]-transformations of A. Jakimovski, Bull. Res. Council Israel, 10F4 (1962), 165–187.Google Scholar
5. Meir, A., On two problems concerning the generalized Lototsky transforms, Can. J. Math., 16 (1964), 339–342.Google Scholar