Abstract
An open problem is to characterize the Fourier coefficients of Zygmund functions. This problem was also explicitly suggested by Nag and later by Teo and Takhtajan-Teo in the course of study of the universal Teichmüller space. By a complex analysis approach, we give a characterization for the Fourier coefficients of a Zygmund function by a quadratic form. Some related topics are also discussed, including those analytic functions with quasiconformal deformation extensions.
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Shen, Y. Fourier coefficients of Zygmund functions and analytic functions with quasiconformal deformation extensions. Sci. China Math. 55, 607–624 (2012). https://doi.org/10.1007/s11425-011-4236-3
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DOI: https://doi.org/10.1007/s11425-011-4236-3