DOI QR코드

DOI QR Code

THE GREEN FUNCTION AND THE SZEGŐ KERNEL FUNCTION

Chung, Young-Bok

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

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.

키워드

Green function;Szego kernel;Ahlfors map;Dirichlet problem

참고문헌

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  2. 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
  3. 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
  4. 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
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  6. P. R. Garabedian, Schwarz's lemma and the Szego kernel function, Trans. Amer. Math. Soc. 67 (1949), 1-35.