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arXiv · 2209.01323

Bergman-Szeg\H{o} asymptotic formulas and the strip problem

Mark G. Lawrence
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Abstract

Identifying holomorphic functions by moment conditions is a classical problem. This paper explores ideas introduced by Tumanov in a well known paper on the strip problem, and building on the author's previous work, to show that weighted Bergman projections can be computed via asymptotic formulas involving Szeg\H{o} projections a fixed 1-dimensional family of curves. Various new operators are introduced; in addition, similar formulas are derived via dimension reduction, using the author's CR Hartogs theorem.

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Mark G. Lawrence. 2022-09-03. Bergman-Szeg\H{o} asymptotic formulas and the strip problem. https://arxiv.org/abs/2209.01323

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