Polynomial approximation in the mean with respect to harmonic measure on crescents
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- by John Akeroyd PDF
- Trans. Amer. Math. Soc. 303 (1987), 193-199 Request permission
Abstract:
For $1 \leqslant s < \infty$ and "nice" crescents $G$, this paper gives a necessary condition (Theorem 2.6) and a sufficient condition (Theorem 2.5) for density of the polynomials in the generalized Hardy space ${H^s}(G)$. These conditions are easily tested and almost equivalent.References
- James E. Brennan, Approximation in the mean by polynomials on non-Carathéodory domains, Ark. Mat. 15 (1977), no. 1, 117–168. MR 450566, DOI 10.1007/BF02386037 T. Carleman, Fonctions quasi analytiques, Gauthier-Villars, Paris, 1926.
- J. A. Cima and A. Matheson, Approximation in the mean by polynomials, Rocky Mountain J. Math. 15 (1985), no. 3, 729–738. MR 813271, DOI 10.1216/RMJ-1985-15-3-729
- John B. Conway, Subnormal operators, Research Notes in Mathematics, vol. 51, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1981. MR 634507 T. W. Gamelin, Uniform algebras, 2nd ed., Chelsea, New York, 1984.
- S. N. Mergeljan, On the completeness of systems of analytic functions, Amer. Math. Soc. Transl. (2) 19 (1962), 109–166. MR 0131561
- M. Tsuji, Potential theory in modern function theory, Chelsea Publishing Co., New York, 1975. Reprinting of the 1959 original. MR 0414898
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 303 (1987), 193-199
- MSC: Primary 30D55; Secondary 30E10, 41A10, 46E15, 47B38
- DOI: https://doi.org/10.1090/S0002-9947-1987-0896016-X
- MathSciNet review: 896016