Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614667 | Journal of Mathematical Analysis and Applications | 2016 | 26 Pages |
Abstract
Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence M=(Mp)p∈N0M=(Mp)p∈N0, have been put forward by A. Lastra, S. Malek and the second author [28]. We study several open questions related to the existence of kernels of summability constructed by means of analytic proximate orders. In particular, we give a simple condition that allows us to associate a proximate order with a strongly regular sequence. Under this assumption, and through the characterization of strongly regular sequences in terms of so-called regular variation, we show that the growth index γ(M)γ(M) defined by V. Thilliez [54] and the order of quasianalyticity ω(M)ω(M) introduced by the second author [50] are the same.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Javier Jiménez-Garrido, Javier Sanz,