Solution of the Dirichlet problem by interpolating harmonic polynomials

Author:
J. H. Curtiss

Journal:
Bull. Amer. Math. Soc. **68** (1962), 333-337

DOI:
https://doi.org/10.1090/S0002-9904-1962-10795-2

MathSciNet review:
0146401

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References | Additional Information

**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.**2.**J. L. Walsh,*On interpolation to harmonic functions by harmonic polynomials*, Proc. Nat. Acad. Sci. U.S.A. 18 (1932), 514-517.**3.**J. H. Curtiss,*Interpolation with harmonic and complex polynomials to boundary values*, J. Math. Mech. 9 (1960), 167-192. MR**114060****4.**J. L. Walsh,*Solution of the Dirichlet problem for the ellipse by interpolating harmonic polynomials*, J. Math. Mech. 9 (1960), 193-196. MR**114061****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. MR**125969****6.**S. N. Mergelyan,*Uniform approximations to functions of a complex variable*, Uspehi Mat. Nauk (N.S.), 7 (1952), no. 2 (48), 31-122. Amer. Math. Soc. Transl. No. 101 (1954). MR**51921****7.**J. L. Walsh,*Maximal convergence of sequences of harmonic polynomials*, Ann. of Math. (2)**38**(1937), no. 2, 321–354. MR**1503339**, https://doi.org/10.2307/1968557

Additional Information

DOI:
https://doi.org/10.1090/S0002-9904-1962-10795-2