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Solution of the Dirichlet problem by interpolating harmonic polynomials. (English) Zbl 0107.06001


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[1] J. L. Walsh, The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions, Bull. Amer. Math. Soc. 35 (1929), 499-544. · JFM 55.0889.05
[2] J. L. Walsh, On interpolation to harmonic functions by harmonic polynomials, Proc. Nat. Acad. Sci. U.S.A. 18 (1932), 514-517. · Zbl 0005.01703
[3] J. H. Curtiss, Interpolation with harmonic and complex polynomials to boundary values., J. Math. Mech. 9 (1960), 167 – 192. · Zbl 0092.29301
[4] J. L. Walsh, Solution of the Dirichlet problem for the ellipse by interpolating harmonic polynomials, J. Math. Mech. 9 (1960), 193 – 196. · Zbl 0092.29302
[5] W. E. Sewell, Degree of approximation to a continuous function on a non-analytic curve, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 195 – 202. · Zbl 0096.27202
[6] S. N. Mergelyan, Uniform approximations of functions of a complex variable, Uspehi Matem. Nauk (N.S.) 7 (1952), no. 2(48), 31 – 122 (Russian). · Zbl 0059.05902
[7] J. L. Walsh, Maximal convergence of sequences of harmonic polynomials, Ann. of Math. (2) 38 (1937), no. 2, 321 – 354. · Zbl 0017.10801 · doi:10.2307/1968557
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