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Abstract Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence M = ( M p ) p ∈ N 0 , have been put… Click to show full abstract
Abstract Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence M = ( M p ) p ∈ N 0 , have been put forward by A. Lastra, S. Malek and the second author [10] , and their validity depends on the possibility of associating to M a nonzero proximate order. We provide several characterizations of this and other related properties, in which the concept of regular variation for functions and sequences plays a prominent role. In particular, we show how to construct well-behaved strongly regular sequences from nonzero proximate orders.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
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