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Non-extendable Zero Sets of Harmonic and Holomorphic Functions

  • P. M. Gauthier (a1)

Abstract

In this paper we study the zero sets of harmonic functions on open sets in ${{\mathbb{R}}^{N}}$ and holomorphic functions on open sets in ${{\mathbb{C}}^{N}}$ . We show that the non-extendability of such zero sets is a generic phenomenon.

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[1] Bernal-Gonzâlezand, L. Ordonez Cabrera, M., Lineability criteria, with applications.J. Funct. Anal. 266(2014), no. 6, 39974025.http://dx.doi.org/10.1016/j.jfa.2O13.11.014
[2] Gardiner, S. J., Harmonic approximation.London Math. Soc. Lecture Notes Series, 221, Cambridge University Press, Cambridge, 1995.
[3] Manne, P. E., E. E Wold, and N. 0vrelid, Holomorphic convexity and Carleman approximation by entire functions on Stein manifolds. Math. Ann. 351(2011), 571585. http://dx.doi.org/!0.1007/s00208-010-0605-4
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Non-extendable Zero Sets of Harmonic and Holomorphic Functions

  • P. M. Gauthier (a1)

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