Email this article The logarithmic energy of zeros and poles of a rational function
- Authors: Dubinin V.N.1
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Affiliations:
- Far-Eastern Federal University, Institute of Applied Mathematics
- Issue: Vol 57, No 6 (2016)
- Pages: 981-986
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170828
- DOI: https://doi.org/10.1134/S0037446616060057
- ID: 170828
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Abstract
On assuming that certain lemniscates of a rational function are connected, we establish some sharp inequality that involves the logarithmic energy of a discrete charge concentrated at the zeros and poles of this function and the absolute values of its derivatives at these points. The equality in this estimate is attained for specially arranged zeros and poles of a suitable Zolotarev fraction and for special distributions of charge.
About the authors
V. N. Dubinin
Far-Eastern Federal University, Institute of Applied Mathematics
Author for correspondence.
Email: dubinin@iam.dvo.ru
Russian Federation, Vladivostok
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