کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4614705 | 1339297 | 2015 | 11 صفحه PDF | دانلود رایگان |
We investigate the sets of uniform limits A(B‾n), A(D‾I) of polynomials on the closed unit ball B‾n of CnCn and on the cartesian product D‾I where I is an arbitrary set, maybe finite, infinite denumerable or non-denumerable and D‾ is the closed unit disc in CC. The class A(D‾I) contains exactly all functions f:D‾I→C continuous with respect to the product topology on D‾I and separately holomorphic. We consider sets of uniqueness for A(D‾I) (respectively for A(B‾n)) to be compact subsets K of TITI (respectively of ∂B‾n) where T=∂DT=∂D is the unit circle. If K has positive measure then K is a set of uniqueness. The converse does not hold. Finally, we do a similar study when the uniform convergence is not meant with respect to the usual Euclidean metric in CC, but with respect to the chordal metric χ on C∪{∞}C∪{∞}.
Journal: Journal of Mathematical Analysis and Applications - Volume 432, Issue 2, 15 December 2015, Pages 994–1004