On approximation by bounded analytic functions
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References
- J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587 —, On interpolation and approximation by functions analytic and bounded in a given region, Proc. Nat. Acad. Sci. U.S.A., vol. 24 (1938) pp. 477-486.
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- W. E. Sewell, Degree of Approximation by Polynomials in the Complex Domain, Annals of Mathematics Studies, No. 9, Princeton University Press, Princeton, N. J., 1942. MR 0007054
- E. N. Nilson and J. L. Walsh, Interpolation and approximation by functions analytic and bounded in a given region, Trans. Amer. Math. Soc. 55 (1944), 53–67. MR 9196, DOI 10.1090/S0002-9947-1944-0009196-7
- J. L. Walsh, Taylor’s series and approximation to analytic functions, Bull. Amer. Math. Soc. 52 (1946), 572–579. MR 17362, DOI 10.1090/S0002-9904-1946-08615-2
- J. L. Walsh, W. E. Sewell, and H. M. Elliott, On the degree of polynomial approximation to harmonic and analytic functions, Trans. Amer. Math. Soc. 67 (1949), 381–420. MR 33920, DOI 10.1090/S0002-9947-1949-0033920-5
- J. L. Walsh and H. Margaret Elliott, Polynomial approximation to harmonic and analytic functions: generalized continuity conditions, Trans. Amer. Math. Soc. 68 (1950), 183–203. MR 33921, DOI 10.1090/S0002-9947-1950-0033921-5
- J. L. Walsh, Note on approximation by bounded analytic functions, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 821–826. MR 45206, DOI 10.1073/pnas.37.12.821
- J. L. Walsh and H. Margaret Elliott, Degree of approximation on a Jordan curve, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 1058–1066. MR 53229, DOI 10.1073/pnas.38.12.1058
- H. Margaret Elliott, On approximation to analytic functions by rational functions, Proc. Amer. Math. Soc. 4 (1953), 161–167. MR 54022, DOI 10.1090/S0002-9939-1953-0054022-4
- J. L. Walsh, On the conformal mapping of multiply connected regions, Trans. Amer. Math. Soc. 82 (1956), 128–146. MR 80727, DOI 10.1090/S0002-9947-1956-0080727-2
- J. L. Walsh, Sur l’approximation par fonctions rationnelles et par fonctions holomorphes bornées, Ann. Mat. Pura Appl. (4) 39 (1955), 267–277 (French). MR 77684, DOI 10.1007/BF02410774
- J. L. Walsh, Note on degree of approximation to analytic functions by rational functions with preassigned poles, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 927–930. MR 82552, DOI 10.1073/pnas.42.12.927
Additional Information
- © Copyright 1958 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 87 (1958), 467-484
- MSC: Primary 30.00; Secondary 41.00
- DOI: https://doi.org/10.1090/S0002-9947-1958-0096816-4
- MathSciNet review: 0096816