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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
MathSciNet review: 0419777
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Abstract: In this paper we construct a doubly connected domain $D \backepsilon 0$ 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?)

  • Dov Aharonov and Harold S. Shapiro, Domains on which analytic functions satisfy quadrature identities, J. Analyse Math. 30 (1976), 39–73. MR 447589, DOI
  • ---, A minimal area problem in conformal mapping, Royal Inst. Tech. Res. Bull., 1973, 34 pp.
  • S. N. Mergelyan, On completeness of systems of analytic functions, Uspehi Matem. Nauk (N.S.) 8 (1953), no. 4(56), 3–63 (Russian). MR 0058698
  • J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587

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Article copyright: © Copyright 1976 American Mathematical Society