Taiwanese Journal of Mathematics

Cross Theorems for Separately $(\cdot, W)$-meromorphic Functions

Thai Thuan Quang and Lien Vuong Lam

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It is shown that Rothstein's theorem holds for $(F, W)$-meromorphic functions with $F$ is a sequentially complete locally convex space. We also prove that a meromorphic function on a Riemann domain $D$ over a separable Banach $E$ with values in a sequentially complete locally convex space can be extended meromorphically to the envelope of holomorphy $\widehat{D}$ of $D$. Using these results, in the remaining parts, we give a version of Kazarian's theorem for the class of separately $(\cdot, W)$-meromorphic functions with values in a sequentially complete locally convex space and generalize cross theorem with pluripolar singularities of Jarnicki and Pflug for separately $(\cdot, W)$-meromorphic functions with values in a Fréchet space.

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Taiwanese J. Math., Volume 20, Number 5 (2016), 1009-1039.

First available in Project Euclid: 1 July 2017

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Primary: 30D30: Meromorphic functions, general theory 32A10: Holomorphic functions 32B10: Germs of analytic sets, local parametrization 46A04: Locally convex Fréchet spaces and (DF)-spaces 46E50: Spaces of differentiable or holomorphic functions on infinite- dimensional spaces [See also 46G20, 46G25, 47H60]

meromorphic functions holomorphic functions plurisubharmonic functions pluripolar set locally pluriregular set locally convex space


Thuan Quang, Thai; Vuong Lam, Lien. Cross Theorems for Separately $(\cdot, W)$-meromorphic Functions. Taiwanese J. Math. 20 (2016), no. 5, 1009--1039. doi:10.11650/tjm.20.2016.7363. https://projecteuclid.org/euclid.twjm/1498874514

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