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BERGMAN-SZEGŐ ASYMPTOTIC FORMULAS AND THE STRIP PROBLEM

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Abstract

Let \(C_t\) be the translate of a fixed curve in a horizontal strip. When a function has holomorphic extensions from each \(C_t\), it is sometimes possible to deduce that the function is holomorphic. We improve previous results to a weighted \(L^2\) setting. This implies the existence of novel asymptotic expressions for Bergman projections, using szegö operators on the curves. Some examples in higher dimensions are demonstrated.

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References

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  1. Nazarbayev University, Astana, Kazakhstan

    Mark G. Lawrence

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  1. Mark G. Lawrence
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Correspondence to Mark G. Lawrence.

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Lawrence, M.G. BERGMAN-SZEGŐ ASYMPTOTIC FORMULAS AND THE STRIP PROBLEM. J Math Sci 280, 109–116 (2024). https://doi.org/10.1007/s10958-023-06764-9

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  • DOI: https://doi.org/10.1007/s10958-023-06764-9

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