2016•arXiv (Cornell University)Open access

Discrete sequences in unbounded domains

Alberto Saracco

Abstract

Discrete sequences with respect to the Kobayashi distance in a strongly pseudoconvex bounded domain $D$ are related to Carleson measures by a formula that uses the Euclidean distance from the boundary of $D$. Thus the speed of escape at the boundary of such sequence has been studied in details for strongly pseudoconvex bounded domain $D$. In this note we show that such estimations completely fail if the domain is not bounded.

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Key concepts: Bounded function, Domain (mathematical analysis), Boundary (topology), Mathematics, Euclidean geometry, Sequence (biology), Euclidean distance, Mathematical analysis