호남수학학술지 (Honam Mathematical Journal)

  • 제36권3호
  • /
  • Pages.659-668
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  • 2014
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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THE GREEN FUNCTION AND THE SZEGŐ KERNEL FUNCTION

  • 투고 : 2014.07.31
  • 심사 : 2014.08.29
  • 발행 : 2014.09.25
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초록

In this paper, we express the Green function in terms of the classical kernel functions in potential theory. In particular, we obtain a formula relating the Green function and the Szegő kernel function which consists of only the Szegő kernel function in a $C^{\infty}$ smoothly bounded finitely connected domain in the complex plane.

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참고문헌

  1. S. Bell, Solving the Dirichlet problem in the plane by means of the Cauchy integral, Indiana Univ. Math. J. 39(4) (1990), 1355-1371. https://doi.org/10.1512/iumj.1990.39.39060
  2. Steve Bell, The Szego projection and the classical objects of potential theory in the plane, Duke Math. J. 64(1) (1991), 1-26. MR MR1131391 (93e:30018) https://doi.org/10.1215/S0012-7094-91-06401-X
  3. Steve Bell, The Szego projection and the classical objects of potential theory in the plane, Duke Math. J. 64(1) (1991), 1-26. https://doi.org/10.1215/S0012-7094-91-06401-X
  4. Steven R. Bell, Ahlfors maps, the double of a domain, and complexity in potential theory and conformal mapping, J. Anal. Math. 78 (1999), 329-344. MR 1714417 (2000m:30012) https://doi.org/10.1007/BF02791140
  5. Stefan Bergman, The Kernel Function and Conformal Mapping, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR 0038439 (12, 402a)
  6. P. R. Garabedian, Schwarz's lemma and the Szego kernel function, Trans. Amer. Math. Soc. 67 (1949), 1-35.