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MATHEMATICS
Potential theory on an analytic surface
B. I. Abdullaevab, Kh. Q. Kamolova a Urgench State University, ul. Kh. Alimdjana, 14, Urgench, 220100, Uzbekistan
b V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences,
Khorezm Branch, ul. Kh. Alimdjana, 14, Urgench, 220100, Uzbekistan
Abstract:
The work is devoted to the theory of pluripotential on analytic surfaces. The pluripotential theory on the complex space ${\mathbb C}^{n},$ as well as on the Stein complex manifold $X\subset{\mathbb C}^{N}$ (without a singular set) have been studied in enough detail. In this work, we propose a new approach for studying the main objects of potential theory on an analytic set with a non-empty singular (critical) set.
Keywords:
analytic set, plurisubharmonic function, pluripolar set, ${\mathcal{P}}$-measure, maximal function.
Received: 04.10.2022 Accepted: 27.12.2022
Citation:
B. I. Abdullaev, Kh. Q. Kamolov, “Potential theory on an analytic surface”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:1 (2023), 3–16
Linking options:
https://www.mathnet.ru/eng/vuu832 https://www.mathnet.ru/eng/vuu/v33/i1/p3
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Abstract page: | 166 | Full-text PDF : | 50 | References: | 23 |
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