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THE BERGMAN KERNEL FUNCTION AND THE SZEGO KERNEL FUNCTION
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 Title & Authors
THE BERGMAN KERNEL FUNCTION AND THE SZEGO KERNEL FUNCTION
CHUNG YOUNG-BOK;
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 Abstract
We compute the holomorphic derivative of the harmonic measure associated to a bounded domain in the plane and show that the exact Bergman kernel function associated to a bounded domain in the plane relates the derivatives of the Ahlfors map and the Szego kernel in an explicit way. We find several formulas for the exact Bergman kernel and the Szego kernel and the harmonic measure. Finally we survey some other properties of the holomorphic derivative of the harmonic measure. 缀Ѐ㘰〻ሀ䝥湥牡氠瑥捨湯汯杹
 Keywords
Bergman kernel;Szego kernel;Ahlfors map;harmonic measure;
 Language
English
 Cited by
 References
1.
S. Bell, Solving the Dirichlet problem in the plane by means of the Cauchy integral, Indiana Univ. Math. J. 39 (1990), no. 4, 1355-1371 crossref(new window)

2.
S. Bell, Recipes for classical kernel functions associated to a multiply connected domain in the plane, Complex Variables Theory Appl. 29 (1996), no. 4, 367-378 crossref(new window)

3.
S. Bell, The Szego projection and the classical objects of potential theory in the plane, Duke Math. J. 64 (1991), no. 1, 1-26 crossref(new window)

4.
S. Bell, The Cauchy transform, potential theory, and conformal mapping, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992

5.
S. Bell, Complexity of the classical kernel functions of potential theory, Indiana Univ. Math. J. 44 (1995), no. 4, 1337-1369

6.
Stefan Bergman, The kernel function and conformal mapping, Second, revised edition. Mathematical Surveys, No. V. American Mathematical Society, Providence, R.I., 1970

7.
Y. -B. Chung, The Bergman kernel function and the Ahlfors mapping in the plane, Indiana Univ. Math. J. 42 (1993), 1339-1348 crossref(new window)

8.
Y. -B. Chung, An expression of the Bergman kernel function in terms of the Szego kernel, J. Math. Pures Appl. 75 (1996), 1-7

9.
P. R. Garabedian, Schwarz's lemma and the Szego kernel function, Trans. Amer. Math. Soc. 67 (1949), 1-35 crossref(new window)

10.
Dennis A. Hejhal, Theta functions, kernel functions, and Abelian integrals, Memoirs of the American Mathematical Society, No. 129. American Mathematical Society, Providence, R.I., 1972

11.
N. Kerzman and E. M. Stein, The Cauchy kernel, the Szego kernel, and the Riemann mapping function, Math. Ann. 236 (1978), no. 1, 85-93 crossref(new window)

12.
N. Kerzman and M. R. Trummer, Numerical conformal mapping via the Szego kernel, Special issue on numerical conformal mapping. J. Comput. Appl. Math. 14 (1986), no. 1-2, 111-123 crossref(new window)

13.
Saburou Saitoh, Theory of reproducing kernels and its applications, Pitman Research Notes in Mathematics Series, 189. Longman Scientific & Technical, Harlow, 1988

14.
Menahem Schiffer, Various types of orthogonalization, Duke Math. J. 17 (1950), 329-366 crossref(new window)

15.
M. Trummer, An efficient implementation of a conformal mapping method based on the Szego kernel, SIAM J. Numer. Anal. 23 (1986), no. 4, 853-872 crossref(new window)