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Finitely generated function fields and complexity in potential theory in the plane
Steven R. Bell
Source: Duke Math. J. Volume 98, Number 1
(1999), 187-207.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077228055
Mathematical Reviews number (MathSciNet): MR1687563
Zentralblatt MATH identifier: 0948.30015
Digital Object Identifier: doi:10.1215/S0012-7094-99-09805-8
References
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Mathematical Reviews (MathSciNet): MR22:5729
Zentralblatt MATH: 0196.33801
[2] Steven Bell, Proper holomorphic mappings that must be rational, Trans. Amer. Math. Soc. 284 (1984), no. 1, 425–429.
Mathematical Reviews (MathSciNet): MR85k:32047
Zentralblatt MATH: 0541.32009
Digital Object Identifier: doi:10.2307/1999295
JSTOR: links.jstor.org
[3] Steve Bell, Proper holomorphic correspondences between circular domains, Math. Ann. 270 (1985), no. 3, 393–400.
Mathematical Reviews (MathSciNet): MR86j:32053
Zentralblatt MATH: 0554.32019
Digital Object Identifier: doi:10.1007/BF01473434
[4] Steve Bell, The Szegő projection and the classical objects of potential theory in the plane, Duke Math. J. 64 (1991), no. 1, 1–26.
Mathematical Reviews (MathSciNet): MR93e:30018
Zentralblatt MATH: 0739.31002
Digital Object Identifier: doi:10.1215/S0012-7094-91-06401-X
Project Euclid: euclid.dmj/1077295384
[5] Steven R. Bell, The Cauchy transform, potential theory, and conformal mapping, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992.
Mathematical Reviews (MathSciNet): MR94k:30013
[6] Steven R. Bell, Complexity of the classical kernel functions of potential theory, Indiana Univ. Math. J. 44 (1995), no. 4, 1337–1369.
Mathematical Reviews (MathSciNet): MR97g:30009
Zentralblatt MATH: 0862.31001
Digital Object Identifier: doi:10.1512/iumj.1995.44.2030
[7] S. Bell, A Riemann surface attached to domains in the plane and complexity in potential theory, to appear.
Mathematical Reviews (MathSciNet): MR1814239
Zentralblatt MATH: 0981.30007
[8] Stefan Bergman, The Kernel Function and Conformal Mapping, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950.
Mathematical Reviews (MathSciNet): MR12,402a
Zentralblatt MATH: 0040.19001
[9] Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948.
Mathematical Reviews (MathSciNet): MR10,366a
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[10] Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York, 1980.
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[11] Dennis A. Hejhal, Theta functions, kernel functions, and Abelian integrals, American Mathematical Society, Providence, R.I., 1972, Mem. Amer. Math. Soc., no. 129.
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[12] Olli Lehto, Univalent functions and Teichmüller spaces, Graduate Texts in Mathematics, vol. 109, Springer-Verlag, New York, 1987.
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[13] Menahem Schiffer, Various types of orthogonalization, Duke Math. J. 17 (1950), 329–366.
Mathematical Reviews (MathSciNet): MR12,491g
Zentralblatt MATH: 0039.08602
Digital Object Identifier: doi:10.1215/S0012-7094-50-01731-5
Project Euclid: euclid.dmj/1077476226
[14] Harold S. Shapiro, The Schwarz function and its generalization to higher dimensions, University of Arkansas Lecture Notes in the Mathematical Sciences, 9, John Wiley & Sons Inc., New York, 1992.
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Zentralblatt MATH: 0784.30036
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