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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0262514-8
MathSciNet review:
0262514
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- Georg Faber, Über polynomische Entwickelungen, Math. Ann. 57 (1903), no. 3, 389–408 (German). MR 1511216, DOI https://doi.org/10.1007/BF01444293
- W. F. Newns, On the representation of analytic functions by infinite series, Philos. Trans. Roy. Soc. London Ser. A 245 (1953), 429–468. MR 54717, DOI https://doi.org/10.1098/rsta.1953.0003
- W. F. Newns, 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 0110817
- W. F. Newns, The range of effectiveness of a basic set, Proc. London Math. Soc. (3) 18 (1968), 745–767. MR 232002, DOI https://doi.org/10.1112/plms/s3-18.4.745
- J.-M. Whittaker, Sur les Séries de Base de Polynomes Quelconques, Gauthier-Villars, Paris, 1949 (French). Avec la collaboration de C. Gattegno. MR 0032769
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30.70
Retrieve articles in all journals with MSC: 30.70
Additional Information
Keywords:
Expansion in polynomials,
simple set of polynomials,
Faber regions
Article copyright:
© Copyright 1970
American Mathematical Society