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Some Regular [F, dn] Matrices with Complex Elements

Published online by Cambridge University Press:  20 November 2018

Chester L. Miracle*
Affiliation:
University of Minnesota
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Let A = (ank) and {sn} (n, k = 0, 1, 2, . . .) be a matrix and a sequence of complex numbers, respectively. Let the members of the sequence {σn} be defined by

then we say {σn} is the A -transform of {sn}. The matrix A = (ank) is called regular if

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Agnew, R. P., Eider transformations, Amer. J. Math., 66 (1944), 318338.Google Scholar
2. Cowling, V. F., Summability and analytic continuation, Proc. Amer. Math. Soc, 1 (1950), 536542.Google Scholar
3. Cowling, V. F. and Miracle, C. L., Some results on the generalized Lototsky transform, Can. j . Math., 14 (1962), 418435.Google Scholar
4. Jakimovski, A., A generalization of the Lototsky method of summability, Michigan Math. J., 6 (1959), 277290.Google Scholar
5. Lototsky, A. V., On a linear transformation of sequences and series, Ivanor, Gos. Ped. Inst. Uc. Zap. Fig-Mat. Nauki, 4 (1953), 6191 (in Russian).Google Scholar
6. Meir, A., On a theorem of A. Jakimovski on linear transformations, Michigan Math. J., 6 (1959), 359361.Google Scholar
7. Titchmarsh, E. C., Theory of functions (Oxford, 1939).Google Scholar