Year: 2025
Type: article
Abstract: In 1930, S. N. Bernstein proved the following theorem: Let 𝑓 and 𝐹 be complex polynomials such that 1) deg 𝑓 deg 𝐹 " 𝑛; 2) 𝐹 has all its zeros in closure of the disc Δ " t𝑧 P C :In a huge number of papers that appeared after 1930 and related to this theorem, the restrictions on the geometry of domains and conditions 1) and 2) of the theorem usually remained unchanged.In this article, we consistently remove these restrictions and find out how this will affect the final inequality |𝑓 1 p𝑧q| |𝐹 1 p𝑧q| of the Bernstein theorem and many of its modifications, generalizations, and consequences.
Source: Problemy analiza
Authors: E. G. Kompaneets, V. V. Starkov, E. S. Shmidt
Institution: Petrozavodsk State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416270803
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