논문KCI 등재
Dirichlet problem for polynomials on the unit disk
대한수학회 (The Korean Mathematical Society)|2014.07|대한수학회논문집 (Communications of the KMS)|제29권 제3호|pp. 415-420
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참고문헌
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초록
We give explicit formulas, without using the Poisson integral, for the functions that are C-harmonic on the unit disk and restrict to a prescribed polynomial on the boundary.
Abstract
We give explicit formulas, without using the Poisson integral, for the functions that are C-harmonic on the unit disk and restrict to a prescribed polynomial on the boundary.
참고문헌 (8)
- S. Axler, "Harmonic Function Theory" (2001), Springer-Verlag
- S. R. Bell, "On the classical Dirichlet problem in the plane with rational data", J. Anal. Math, 100, pp.157~190 (2006)
- S. R. Bell, "Algebraicity in the Dirichlet problem in the plane with rational data", Complex Var. Elliptic Equ, 52(2-3), pp.235~244 (2007)
- M. Chamberland, "Polynomial solutions to Dirichlet problems", Proc. Amer. Math. Soc, 129(1), pp.211~217 (2001)
- P. Ebenfelt, "An explicit solution to the Dirichlet problem with rational holomorphic data in terms of a Riemann mapping", Comput. Methods Funct. Theory, 7(1), pp.127~140 (2007)
- D. Khavinson, "A tale of ellipsoids in potential theory", Amer. Math. Soc, 61(2), pp.148~156 (2014)
- J. C. Mason, "Chebyshev Polynomials", pp.2003, Chapman & Hall
- T. J. Rivlin, "The Chebyshev Polynomials, Pure and Applied Mathematics" (1974), Wiley-Interscience
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