Email this article An upper bound for the least critical values of finite Blaschke products
- Authors: Dubinin V.N.1,2
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Affiliations:
- Far Eastern Center of Mathematical Research, Far Eastern Federal University
- Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
- Issue: Vol 213, No 6 (2022)
- Pages: 13-20
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133447
- DOI: https://doi.org/10.4213/sm9600
- ID: 133447
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Abstract
For the finite Blaschke products $B$ of degree $n\geq2$ such that $B(0)=0$ and $ B'(0)\neq0$, the supremum of the minimum moduli of their critical values is found which depends only on $n$ and $|B'(0)|$.Bibliography: 12 titles.
About the authors
Vladimir Nikolaevich Dubinin
Far Eastern Center of Mathematical Research, Far Eastern Federal University; Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
Email: dubinin@iam.dvo.ru
Doctor of physico-mathematical sciences, Professor
References
- Blaschke products and their applications (Toronto, ON, 2011), Fields Inst. Commun., 65, eds. J. Mashreghi, E. Fricain, Springer, New York; Fields Institute for Research in Mathematical Sciences, Toronto, ON, 2013, x+319 pp.
- Tuen Wai Ng, Chiu Yin Tsang, “Chebyshev–Blaschke products: solutions to certain approximation problems and differential equations”, J. Comput. Appl. Math., 277 (2015), 106–114
- Tuen-Wai Ng, Yongquan Zhang, “Smale's mean value conjecture for finite Blaschke products”, J. Anal., 24:2 (2016), 331–345
- S. R. Garcia, J. Mashreghi, W. T. Ross, Finite Blaschke products and their connections, Springer, Cham, 2018, xix+328 pp.
- T. Sheil-Small, Complex polynomials, Cambridge Stud. Adv. Math., 75, Cambridge Univ. Press, Cambridge, 2002, xx+428 pp.
- V. N. Dubinin, “Distortion and critical values of the finite Blaschke product”, Constr. Approx., 55:2 (2022), 629–639
- V. Dimitrov, A proof of the Schinzel–Zassenhaus conjecture on polynomials
- В. Н. Дубинин, “Неравенства для критических значений полиномов”, Матем. сб., 197:8 (2006), 63–72
- S. Smale, “The fundamental theorem of algebra and complexity theory”, Bull. Amer. Math. Soc. (N.S.), 4:1 (1981), 1–36
- В. H. Дубинин, Емкости конденсаторов и симметризация в геометрической теории функций комплексного переменного, Дальнаука, Владивосток, 2009, ix+390 с.
- А. Гурвиц, Р. Курант, Теория функций, Наука, М., 1968, 648 с.
- Дж. Дженкинс, Однолистные функции и конформные отображения, ИЛ, М., 1962, 265 с.
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