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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

Solution of the Dirichlet problem by interpolating harmonic polynomials


Author: J. H. Curtiss
Journal: Bull. Amer. Math. Soc. 68 (1962), 333-337
MathSciNet review: 0146401
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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.
  • 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 0114060
  • 4. J. L. Walsh, Solution of the Dirichlet problem for the ellipse by interpolating harmonic polynomials, J. Math. Mech. 9 (1960), 193–196. MR 0114061
  • 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 0125969
  • 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). MR 0051921
  • 7. J. L. Walsh, Maximal convergence of sequences of harmonic polynomials, Ann. of Math. (2) 38 (1937), no. 2, 321–354. MR 1503339, 10.2307/1968557


Additional Information

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