科研之友
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摘要
It is shown that if A is a uniform algebra generated by a family (13 of complex-valued C-1 functions on a compact C-1 manifold-with-boundary M, the maximal ideal space of A is M, and E is the set of points where the differentials of the functions in Phi fail to span the complexified cotangent space to M, then A contains every continuous function on M that vanishes on E. This answers a 45-year-old question of Michael Freeman who proved the special case in which the manifold M is two-dimensional. More general forms of the theorem are also established. The results presented strengthen results due to several mathematicians.
- 出版日期2011-7
