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- W4377245482 abstract "In this paper, we first consider the graph of $$(F_1,F_{2},ldots ,F_{n})$$ on $$overline{mathbb {D}}^{n},$$ where $$F_{j}(z)=bar{z}^{m_{j}}_{j}+R_{j}(z),j=1,2,ldots ,n,$$ which has non-isolated CR-singularities if $$m_{j}>1$$ for some $$jin {1,2,ldots ,n}.$$ We show that under the certain condition on $$R_{j},$$ the graph is polynomially convex, and holomorphic polynomials on the graph approximate all continuous functions. We also show that there exists an open polydisk D centered at the origin such that the set $${(z^{m_{1}}_{1},ldots , z^{m_{n}}_{n}, bar{z_1}^{m_{n+1}} + R_{1}(z),ldots , bar{z_{n}}^{m_{2n}} + R_{n}(z)):zin overline{D},m_{j}in mathbb {N}, j=1,ldots ,2n}$$ is polynomially convex, and if $$gcd (m_{j},m_{k})=1~~forall jnot =k,$$ the algebra generated by the functions $$z^{m_{1}}_{1},ldots , z^{m_{n}}_{n}, bar{z_1}^{m_{n+1}} + R_{1},ldots , bar{z_{n}}^{m_{2n}} + R_{n}$$ is dense in $$mathcal {C}(overline{D}).$$ We prove an analogue of Minsker’s theorem over the closed unit polydisk, i.e., if $$gcd (m_{j},m_{k})=1~~forall jnot =k,$$ the algebra $$[z^{m_{1}}_{1},ldots , z^{m_{n}}_{n}, bar{z_1}^{m_{n+1}},ldots , bar{z_{n}}^{m_{2n}};{overline{mathbb {D}}^{n}} ]=mathcal {C}(overline{mathbb {D}}^{n}).$$" @default.
- W4377245482 created "2023-05-23" @default.
- W4377245482 creator A5076343387 @default.
- W4377245482 date "2023-05-22" @default.
- W4377245482 modified "2023-09-23" @default.
- W4377245482 title "Polynomial Convexity and Polynomial Approximations of Certain Sets in $$mathbb {C}^{2n}$$ with Non-isolated CR-Singularities" @default.
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- W4377245482 doi "https://doi.org/10.1007/s12220-023-01303-z" @default.
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