Abstract
Twenty years ago JohnWermer and the author [4] proved a theorem on approximation by analytic functions on a totally real submanifold of Cn. One part of the argument was quite precise and assumed only that the manifold was of class C1. However, another part using L2 estimates required higher differentiability assumptions, depending on the dimension n.
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References
[1] Bo Berndtsson, Integral kernels and approximation on totally real submanifold of Cn, Report Dept. of Math. Gothenburg (1979), no. 1, 8 pp..
[2] F. Reese Harvey and R. O. Wells, Jr, Holomorphic approximation and hyperfunction theory on a C1 totally real submanifold of a complex manifold, Math. Ann. 197 (1972), 287–318.
[3] L. Hörmander, The analysis of linear partial differential operators I. Distribution theory, Springer Verlag, Berlin, Heidelberg, New York, Tokyo, 1983.
[4] L. Hörmander and J. Wermer, Uniform approximation on compact sets in Cn, Math. Scand. 23 (1968), 5–21.
[5] F. A. Valentine, A Lipschitz condition preserving extensions of a vector function, Amer. J. Math. 67 (1945), 83–93.
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Hörmander, L. (2018). Approximation On Totally Real Manifolds. In: Unpublished Manuscripts . Springer, Cham. https://doi.org/10.1007/978-3-319-69850-2_12
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DOI: https://doi.org/10.1007/978-3-319-69850-2_12
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