An inequality for the norm of a polynomial factor

Author:
Igor E. Pritsker

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2283-2291

MSC (1991):
Primary 30C10, 30C85; Secondary 11C08, 31A15

DOI:
https://doi.org/10.1090/S0002-9939-00-05818-4

Published electronically:
November 30, 2000

MathSciNet review:
1823911

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Abstract | References | Similar Articles | Additional Information

Let be a monic polynomial of degree , with complex coefficients, and let be its monic factor. We prove an asymptotically sharp inequality of the form , where denotes the sup norm on a compact set in the plane. The best constant in this inequality is found by potential theoretic methods. We also consider applications of the general result to the cases of a disk and a segment.

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Additional Information

**Igor E. Pritsker**

Affiliation:
Department of Mathematics, 401 Mathematical Sciences, Oklahoma State University, Stillwater, Oklahoma 74078-1058

Email:
igor@math.okstate.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05818-4

Keywords:
Polynomials,
uniform norm,
logarithmic capacity,
equilibrium measure,
subharmonic function,
Fekete points

Received by editor(s):
November 8, 1999

Received by editor(s) in revised form:
November 23, 1999

Published electronically:
November 30, 2000

Additional Notes:
Research supported in part by the National Science Foundation grants DMS-9996410 and DMS-9707359.

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 2000
American Mathematical Society