### FUNCTION ALGEBRAS ON BIDISKS

Chi, Kieu Phuong;Dieu, Nguyen Quang

• 투고 : 2010.05.11
• 발행 : 2012.03.31
• 13 8

#### 초록

We study sufficient conditions for function algebras generated by four smooth functions on a small closed bidisk near the origin in $\mathbb{C}$ to coincide with the space of continuous functions on the bidisk. This problem in one dimension has been studied by De Paepe and the second name author.

#### 키워드

function algebras;polynomially convex;approximation on disks

#### 참고문헌

1. N. Q. Dieu and K. P. Chi, Function algebras on disks II, Indag. Math. (NS). 17 (2006), no. 4, 557-566. https://doi.org/10.1016/S0019-3577(07)00005-5
2. N. Q. Dieu and P. J. de Paepe, Function algebras on disks, Complex Var. Theory Appl. 47 (2002), no. 5, 447-451. https://doi.org/10.1080/02781070290013848
3. L. Hormander and J. Wermer, Uniform approximation on compact sets in Cn, Math. Scand. 23 (1968), 5-21. https://doi.org/10.7146/math.scand.a-10893
4. A. G. O'Farrell, K.J. Preskenis, and D. Walsh, Holomorphic approximation in Lipschitz norms, Proceedings of the conference on Banach algebras and several complex variables (New Haven, Conn., 1983), 187-194, Contemp. Math., 32, Amer. Math. Soc., Providence, RI, 1984.
5. P. J. de Paepe, Eva Kallin's lemma on polynomial convexity, Bull. London Math. Soc. 33 (2001), no. 1, 1-10. https://doi.org/10.1112/blms/33.1.1