A Note on the Density of Rational Functions in A(Ω)

Chapter
Part of the Fields Institute Communications book series (FIC, volume 81)

Abstract

We present a sufficient condition to ensure the density of the set of rational functions with prescribed poles in the algebra A (Ω).

Keywords

Padé approximation Rational functions Rational approximation 

2010 Mathematics Subject Classification.

Primary 30K05 30E10; Secondary 51M99 

Notes

Acknowledgements

The fist author was supported by FNRS project T.0164.16.

References

  1. 1.
    Brezinski, C. History of continued fractions and Padé approximants. Springer Series in Computational Mathematics, 12. Springer-Verlag, Berlin, 1991. vi+551 pp. ISBN: 3-540-15286-5.Google Scholar
  2. 2.
    Costakis, G., Nestoridis, V., Papadoperakis, I. Universal Laurent series. Proc. Edinb. Math. Soc. (2), 48(3), (2005) 571–583.Google Scholar
  3. 3.
    Daras, N., Fournodavlos, G., Nestoridis, V. Universal Padé approximants on simply connected domains. arxiv:1501.02381 (2015) (preprint).Google Scholar
  4. 4.
    Daras, N., Nestoridis, V., Papadimitropoulos, C. Universal Padé approximants of Seleznev type. Arch. Math. (Basel) 100 (2013), no. 6, 571–585.Google Scholar
  5. 5.
    Diamantopoulos, E., Mouratides, CH., Tsirivas, N. Universal Taylor series on unbounded open sets, Analysis (Munich) 26 (3) (2006) 323–326.Google Scholar
  6. 6.
    Falcó, J., Nestoridis, V. A Runge type theorem for product of planar domains. RACSAM (2016). doi:10.1007/s13398-016-0353-8.Google Scholar
  7. 7.
    Falcó, J., Nestoridis, V. Rational approximation on A (Ω) (submitted).Google Scholar
  8. 8.
    Gauthier, P. M., Nestoridis, V. Density of polynomials in classes of functions on products of planar domains. J. Math. Anal. Appl. 433 (2016), no. 1, 282–290.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Nestoridis, V., Zadik, I. Padé approximants, density of rational functions in A (Ω) and smoothness of the integration operator. J. Math. Anal. Appl. 423 (2015), no. 2, 1514–1539.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Rudin, W. Real and complex analysis. Third edition. McGraw-Hill Book Co., New York. xiv+416 pp. (1987) ISBN: 0-07-054234-1.Google Scholar
  11. 11.
    Saff, E. B. Polynomial and rational approximation in the complex domain. Approximation theory (New Orleans, La., 1986), 21–49, Proc. Sympos. Appl. Math., 36, AMS Short Course Lecture Notes, Amer. Math. Soc., Providence, RI, 1986.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Javier Falcó
    • 1
  • Vassili Nestoridis
    • 2
  • Ilias Zadik
    • 3
  1. 1.Departamento de Análisis MatemáticoUniversidad de ValenciaBurjasotSpain
  2. 2.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece
  3. 3.Operations Research CenterMassachusetts Institute of TechnologyCambridgeUSA

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