Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

The zeros of Faber polynomials
generated by an $m$-star


Author: Arno B. J. Kuijlaars
Journal: Math. Comp. 65 (1996), 151-156
MSC (1991): Primary 30C15; Secondary 65D32
DOI: https://doi.org/10.1090/S0025-5718-96-00684-9
MathSciNet review: 1325869
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the zeros of the Faber polynomials generated by a regular $m$-star are located on the $m$-star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.


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

  • 1 J. Bartolomeo and M. He, On Faber polynomials generated by an $m$-star, Math. Comp. 62 (1994), 277--287. MR 94c:30006
  • 2 A. Ghizzetti and A. Ossicini, Quadrature formulae, Birkhäuser, Basel, 1970. MR 42:4012
  • 3 S. Karlin and W. J. Studden, Tchebycheff systems: with applications in analysis and statistics, Interscience, New York, 1966. MR 34:4757
  • 4 A. B. J. Kuijlaars, Chebyshev type quadrature and zeros of Faber polynomials, J. Comput. Appl. Math. (to appear).
  • 5 F. Peherstorfer, Weight functions which admit Tchebycheff quadrature, Bull. Austral. Math. Soc. 26 (1982), 29--38. MR 84k:65025
  • 6 I. J. Schoenberg and G. Szego, An extremum problem for polynomials, Compositio Math. 14 (1960), 260--268. MR 24:A380
  • 7 J. L. Ullman, A class of weight functions that admit Tchebycheff quadrature, Michigan Math. J. 13 (1966), 417--423. MR 34:5290

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 30C15, 65D32

Retrieve articles in all journals with MSC (1991): 30C15, 65D32


Additional Information

Arno B. J. Kuijlaars
Affiliation: Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Email: arno@fwi.uva.nl

DOI: https://doi.org/10.1090/S0025-5718-96-00684-9
Keywords: Faber polynomials, zero distribution, Chebyshev quadrature
Received by editor(s): June 20, 1994
Additional Notes: Supported by the Netherlands Foundation for Mathematics SMC with financial aid from the Netherlands Organization for the Advancement of Scientific Research NWO
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society