Abstract: Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence , have been put forward by A. Lastra, S. Malek and the second author, and their validity depends on the possibility of associating to 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.

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