Book Review
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MathSciNet review:
1568117
Full text of review:
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Book Information:
Author:
Harold S. Shapiro
Title:
The Schwarz function and its generalization to higher dimensions
Additional book information:
University of Arkansas Lecture Notes in the Mathematical Sciences, vol. 9, Wiley-Interscience, New York, 1992, xi+108 pp., US$59.95. ISBN 0-471-57127-X.
Philip J. Davis, The Schwarz function and its applications, The Carus Mathematical Monographs, No. 17, Mathematical Association of America, Buffalo, N.Y., 1974. MR 0407252
Kurt Friedrichs, On certain inequalities and characteristic value problems for analytic functions and for functions of two variables, Trans. Amer. Math. Soc. 41 (1937), no. 3, 321–364. MR 1501907, DOI 10.1090/S0002-9947-1937-1501907-0
N. Kerzman and E. M. Stein, The Cauchy kernel, the Szegö kernel, and the Riemann mapping function, Math. Ann. 236 (1978), no. 1, 85–93. MR 486468, DOI 10.1007/BF01420257
Zeev Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1952. MR 0045823
Makoto Sakai, Quadrature domains, Lecture Notes in Mathematics, vol. 934, Springer-Verlag, Berlin-New York, 1982. MR 663007
Makoto Sakai, Regularity of a boundary having a Schwarz function, Acta Math. 166 (1991), no. 3-4, 263–297. MR 1097025, DOI 10.1007/BF02398888
- [1]
- P. J. Davis, The Schwarz function and its applications, Carus Math. Monographs, vol. 17, Math. Assoc. Amer., Washington, DC, 1974. MR 0407252 (53:11031)
- [2]
- K. Friedrichs, On certain inequalities for analytic functions and for functions of two variables, Trans. Amer. Math. Soc. 41 (1937), 321-364. MR 1501907
- [3]
- N. Kerzman and E. Stein, The Cauchy kernel, the Szegö kernel, and the Riemann mapping function, Math. Ann. 236 (1978), 85-93. MR 0486468 (58:6199)
- [4]
- Z. Nehari, Conformal mapping, McGraw-Hill, New York, 1952. MR 0045823 (13:640h)
- [5]
- M. Sakai, Quadrature domains, Lecture Notes in Math., vol. 934, Springer, Berlin, 1982. MR 663007 (84h:41047)
- [6]
- -, Regularity of a boundary having a Schwarz function, Acta Math. 166 (1991), 263-297. MR 1097025 (92c:30042)
Review Information:
Reviewer:
J. Korevaar
Journal:
Bull. Amer. Math. Soc.
31 (1994), 112-116
DOI:
https://doi.org/10.1090/S0273-0979-1994-00487-2