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SP Transform and Uniform Convergence of Laurent and Power Series

Published online by Cambridge University Press:  20 November 2018

S.A. Settu
S.A. Settu*
Affiliation:
Ramanujan Institute University of Madras Madras-600 005 India
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Abstract

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If the Laurent series

is transformed to

it is shown that convergence of the former at z = 1 implies the uniform convergence of the latter on a symmetric arc of |z - 1/P| = 1/P - 1 not containing z = 1 and that the uniform convergence of the former over a symmetric arc of |z| = 1 containing z = 1 implies uniform convergence of the latter on the entire circle |z — 1/P| = 1/P — 1.

Keywords

Primary 30B30Secondary 40G99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 114 - 123
Copyright
Copyright © Canadian Mathematical Society 01

References

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