|
The zeros of Faber polynomials generated by an  -star
Author(s):
Arno
B. J.
Kuijlaars.
Journal:
Math. Comp.
65
(1996),
151-156.
MSC (1991):
Primary 30C15;
Secondary 65D32
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
It is shown that the zeros of the Faber polynomials generated by a regular  -star are located on the  -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:
- 1
- J. Bartolomeo and M. He, On Faber polynomials generated by an
 -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
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:
10.1090/S0025-5718-96-00684-9
PII:
S 0025-5718(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
Copyright of article:
Copyright
1996,
American Mathematical Society
|
Comments: webmaster@ams.org