Abstract
We exploit the equality of Bergman analytic content and torsional rigidity of a simply connected domain to develop a new method for calculating these quantities. This method is particularly suitable for the case when the region in question is a polygon. A large number of examples are computed in explicit detail to demonstrate the utility of our ideas.
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Notes
We note that (5) is valid for any domain in \(\varOmega \subseteq \mathbb {C}\) for which the Bergman polynomials form a basis for the Bergman space of \(\varOmega \).
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The authors would like to thank D. Khavinson for useful feedback on a first draft of this manuscript.
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Communicated by Dmitry Khavinson.
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Fleeman, M., Simanek, B. Torsional Rigidity and Bergman Analytic Content of Simply Connected Regions. Comput. Methods Funct. Theory 19, 37–63 (2019). https://doi.org/10.1007/s40315-018-0252-4
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DOI: https://doi.org/10.1007/s40315-018-0252-4