Pluripolarity of graphs of quasianalytic functions in the sense of Gonchar
Sevdiyor Imomkulov, Zafar Ibragimov
TL;DR
This paper proves that graphs of Gonchar's quasianalytic functions on real segments are pluripolar, extending the result to functions on compact subsets of complex space, highlighting their complex-analytic properties.
Contribution
It establishes the pluripolarity of graphs of Gonchar's quasianalytic functions and generalizes this to functions on compact subsets of C^n.
Findings
Graphs of Gonchar's functions are pluripolar.
Generalization to functions on compact subsets of C^n.
Supports complex-analytic structure of quasianalytic functions.
Abstract
We study functions defined on a closed segment of the real line that belong to the class of Gonchar. We show that the graphs of such functions are pluripolar. We also discuss the generalizations of our result to functions defined on a compact subset of C^n that belong to the class of Gonchar.
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Taxonomy
TopicsGeometry and complex manifolds · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods