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Mat. Sb. (N.S.), 1976, Volume 100(142), Number 1(5), Pages 156–164 (Mi msb2866)  

This article is cited in 16 scientific papers (total in 16 papers)

Estimates of the norm of the holomorphic components of functions meromorphic in domains with a smooth boundary

L. D. Grigoryan

Abstract: Let $D$ be a Jordan domain with smooth boundary, $f$ a function meromorphic in $D$, and $f^*$ the holomorphic component of $f$ in $D$. It is shown that $\|f^*\|_{\partial D}\leqslant C(D)n\|f\|_{\partial D}$, where $n$ is the number of poles of $f$ in $D$.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 29:1, 139–146

Bibliographic databases:

UDC: 517.535.6
MSC: 30A68
Received: 01.11.1975

Citation: L. D. Grigoryan, “Estimates of the norm of the holomorphic components of functions meromorphic in domains with a smooth boundary”, Mat. Sb. (N.S.), 100(142):1(5) (1976), 156–164; Math. USSR-Sb., 29:1 (1976), 139–146

Citation in format AMSBIB
\by L.~D.~Grigoryan
\paper Estimates of the norm of the holomorphic components of functions meromorphic in domains with a~smooth boundary
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 100(142)
\issue 1(5)
\pages 156--164
\jour Math. USSR-Sb.
\yr 1976
\vol 29
\issue 1
\pages 139--146

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    This publication is cited in the following articles:
    1. A. A. Gonchar, L. D. Grigoryan, “On estimates of the norm of the holomorphic component of a meromorphic function”, Math. USSR-Sb., 28:4 (1976), 571–575  mathnet  crossref  mathscinet  zmath  isi
    2. E. A. Sevast'yanov, “Rational approximation and absolute convergence of Fourier series”, Math. USSR-Sb., 35:4 (1979), 509–525  mathnet  crossref  mathscinet  zmath  isi
    3. V. V. Peller, “A description of Hankel operators of class $\mathfrak S_p$ for $p>0$, an investigation of the rate of rational approximation, and other applications”, Math. USSR-Sb., 50:2 (1985), 465–494  mathnet  crossref  mathscinet  zmath
    4. V. I. Danchenko, “On separation of singularities of meromorphic functions”, Math. USSR-Sb., 53:1 (1986), 183–201  mathnet  crossref  mathscinet  zmath
    5. A.L Levin, D.S Lubinsky, “Simultaneous rational approximation of a function and its derivatives in the complex plane”, Journal of Approximation Theory, 44:3 (1985), 205  crossref
    6. A. A. Gonchar, L. D. Grigoryan, “On an estimate of the components of bounded analytic functions”, Math. USSR-Sb., 60:2 (1988), 291–295  mathnet  crossref  mathscinet  zmath  isi
    7. A. A. Pekarskii, “Tchebycheff rational approximation in the disk, on the circle, and on a closed interval”, Math. USSR-Sb., 61:1 (1988), 87–102  mathnet  crossref  mathscinet  zmath
    8. D.S Lubinsky, “On the diagonal Padé approximants of meromorphic functions”, Indagationes Mathematicae, 7:1 (1996), 97  crossref
    9. A. A. Pekarskii, “On the Elimination of Singularities of Meromorphic Functions with Finitely Many Poles $p^r$”, Math. Notes, 80:2 (2006), 305–308  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. V. I. Danchenko, “Estimates of derivatives of simplest fractions and other questions”, Sb. Math., 197:4 (2006), 505–524  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. A. A. Pekarskii, “Comparison of the Best Uniform Approximations of Analytic Functions in the Disk and on Its Boundary”, Proc. Steklov Inst. Math., 255 (2006), 215–220  mathnet  crossref  mathscinet
    12. V. I. Danchenko, A. E. Dodonov, “Estimates for exponential sums. Applications”, J Math Sci, 2012  crossref
    13. A. A. Pekarskii, “Conjugate functions and their connection with uniform rational and piecewise-polynomial approximations”, Sb. Math., 206:2 (2015), 333–340  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. J. Math. Sci. (N. Y.), 217:1 (2016), 81–90  mathnet  crossref  mathscinet
    15. D. S. Lubinsky, “Exact interpolation, spurious poles, and uniform convergence of multipoint Padé approximants”, Sb. Math., 209:3 (2018), 432–448  mathnet  crossref  crossref  adsnasa  isi  elib
    16. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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