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An example of a doubly connected domain which admits a quadrature identity


Author: A. L. Levin
Journal: Proc. Amer. Math. Soc. 60 (1976), 163-168
MSC: Primary 30A86; Secondary 30A38
DOI: https://doi.org/10.1090/S0002-9939-1976-0419777-0
MathSciNet review: 0419777
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Abstract: In this paper we construct a doubly connected domain $ D \mathrel\backepsilon 0$ such that $ \smallint {\smallint _D}f(z)d\sigma = Af(0) + Bf'(0)$ for any analytic and area integrable in D function f, which has a single-valued integral in D.


References [Enhancements On Off] (What's this?)

  • [1] Dov Aharonov and Harold S. Shapiro, Domains on which analytic functions satisfy quadrature identities, J. Analyse Math. 30 (1976), 39–73. MR 0447589, https://doi.org/10.1007/BF02786704
  • [2] -, A minimal area problem in conformal mapping, Royal Inst. Tech. Res. Bull., 1973, 34 pp.
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  • [4] J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Third edition. American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
    J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Fourth edition. American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1965. MR 0218588

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DOI: https://doi.org/10.1090/S0002-9939-1976-0419777-0
Article copyright: © Copyright 1976 American Mathematical Society