Uniform algebras and approximation on manifolds
نویسندگان
چکیده
منابع مشابه
Uniform Algebras on Curves
The proofs use the notion of analytic structure in a maximal ideal space. J. Wermer first obtained results along these lines and further contributions were made by E. Bishop and H. Royden and then by G. Stolzenberg [5] who proved STOLZENBERG'S THEOREM. Let XQC be a polynomially convex set. Let KQC be a finite union of Q-curves. Then (XKJK)*—X\JK is a {possibly empty) pure 1-dimensional analytic...
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Let (r); r = 1; 2; : : : be a positive decreasing sequence such that P 1 r=1 (r) k diverges. Using a powerful variance argument due to W. M. Schmidt, an asymptotic formula is obtained for the number of integer solutions q of the system of Diophantine inequalities maxfkqx i k: 1 i kg < (q) which holds for almost all points (x 1 ; : : : ; x k) on a smooth m-dimensional subman-ifold M of R k. The ...
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for 0 ≤ r ≤ k − 1. In particular, dist (f, S π) = O(|π| ) for f ∈ C(I), or, more generally, for f ∈ C(I), such, that f (k−1) satisfies a Lipschitz condition, a result proved earlier by different means [2]. These results are shown to be true even if I is permitted to become infinite and some of the knots are permitted to coalesce. The argument is based on a “local” interpolation scheme Pπ by spl...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2011
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-011-0351-6