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On some polynomial conditions of the type of leja in ¢n

  • Wiesław Pleśniak
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 798)

Abstract

We show that the property of a compact set E in ℂn to satisfy conditions of the type of Leja's famous polynomial condition is invariant under a large class of holomorphic mappings from a neighborhood of the polynomial envelope of E, Ê, to ℂM (M ≤ N) containing, in particular, all open holomorphic mappings. This yields new examples of sets E in ℂN satisfying the conditions under consideration.

Keywords

Lebesgue Measure Holomorphic Mapping Open Neighborhood Borel Subset Extremal Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    JOSEFSON, B.: On the equivalence between locally polar and globally polar sets for plurisubharmonic functions on ℂn, Arkiv för Matematik 16 (1978), 109–115.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    LEJA, F.: Sur les suites de polynômes bornées presque partout sur la frontière d'un domaine, Math. Ann. 108 (1933), 517–524.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    NGUYEN THANH VAN: Familles de polynômes ponctuellement bornées, Ann. Polon. Math. 31 (1975), 83–90.MathSciNetzbMATHGoogle Scholar
  4. [4]
    PLESNIAK, W.: Quasianalytic functions in the sense of Bernstein, Dissertationes Math. 147, (1977), pp. 1–70.MathSciNetzbMATHGoogle Scholar
  5. [5]
    —: Invariance of the L-regularity of compact sets in ℂN under holomorphic mappings, Trans. Amer. Math. Soc. 246 (1978), 373–383.MathSciNetzbMATHGoogle Scholar
  6. [6]
    21 (1979), 97–103.MathSciNetzbMATHGoogle Scholar
  7. [7]
    —: Invariance of some polynomial conditions for compact subsets of ℂN under holomorphic mappings, Zeszyty Nauk. Uniw. Jagiello. 22 (to appear).Google Scholar
  8. [8]
    SICIAK, J.: On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (1962), 322–357.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    —: Extremal plurisubharmonic functions in ℂN, Procedings of the First Finnish-Polish Summer School in Complex Analysis at Podlesice, Vol. I, University of Łódź, Łódź 1977, pp. 115–152.Google Scholar
  10. [10]
    —: On some inequalities for polynomials, Zeszyty Nauk. Uniw. Jagiello. 21 (1979), 7–10.MathSciNetzbMATHGoogle Scholar
  11. [11]
    ZAHARJUTA, V.P.: Extremal pularisubharmonic functions, orthogonal polynomials and Bernstein-Walsh theorem for analytic functions of several complex variables, Ann. Polon. Math. 33 (1976), 137–148 (Russian).MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Wiesław Pleśniak
    • 1
  1. 1.Institute of MathematicsJagiellonian UniversityKrakówPoland

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