On the mean convergence of the Taylor and Laurent series
Abstract
For analytic functions in the domain Δ=D⋃D∞ we find conditions expressed in terms of Laurent coefficients, necessary for convergence in the average of its Laurent series. For functions analytic in a circle ~ D, necessary and sufficient conditions of convergence in the mean Taylor series are obtained, expressed in terms of the coefficients of the Taylor series, and also the boundedness in the metric of the space L1 of partial sums of the Taylor series
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Published
2013-07-15
How to Cite
Tovkach, R. V. (2013). On the mean convergence of the Taylor and Laurent series. Transactions of Institute of Mathematics, the NAS of Ukraine, 10(1), 283–295. Retrieved from https://trim.imath.kiev.ua/index.php/trim/article/view/186
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Research papers