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On the transpose of simple sets of polynomials effective in Faber regions

Author: M. Nassif
Journal: Proc. Amer. Math. Soc. 25 (1970), 209-219
MSC: Primary 30.70
MathSciNet review: 0262514
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Abstract: The effectiveness properties, in a Faber region, of the transpose of simple absolutely monic sets of polynomials effective in the same region, are investigated in the present paper. A lower bound is calculated for an inevitable normalizing factor which ensures the finiteness of the Cannon function of the transpose of the normalized set in the region considered. Yet, except in the case of a circle with centre origin, no value of the normalizing factor can ensure the effectiveness of the transpose in the region considered.

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

  • [1] G. Faber, Über die Polynomische Entwickelung, Math. Ann. 57 (1903), 389-408. MR 1511216
  • [2] W. F. Newns, On the representation of analytic functions by infinite series, Philos. Trans. Roy. Soc. London. Ser. A 245 (1953), 429-468. MR 14, 968. MR 0054717 (14:968b)
  • [3] -, The product of two simple sets effective in a Faber region, Nederl. Akad. Wetensch. Proc. Ser. A 63 = Indag. Math. 22 (1960), 187-191. MR 22 #1685. MR 0110817 (22:1685)
  • [4] -, The range of effectiveness of a basic set, Proc. London Math. Soc. (3) 18 (1968), 745-767. MR 38 #328. MR 0232002 (38:328)
  • [5] J.-M. Whittaker, Sur les séries de base de polynômes quelconques, Gauthier-Villars, Paris, 1939. MR 11, 344. MR 0032769 (11:344a)

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Keywords: Expansion in polynomials, simple set of polynomials, Faber regions
Article copyright: © Copyright 1970 American Mathematical Society

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