On the rank of odd hyper-quasi-polynomials
- Authors: Bykovskii V.A.1
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Affiliations:
- Khabarovsk Branch of Institute of Applied Mathematics, Far East Branch
- Issue: Vol 94, No 2 (2016)
- Pages: 527-528
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224245
- DOI: https://doi.org/10.1134/S1064562416050124
- ID: 224245
Cite item
Abstract
Given any nonzero entire function g: ℂ → ℂ, the complex linear space F(g) consists of all entire functions f decomposable as f(z + w)g(z - w)=φ1(z)ψ1(w)+∙∙∙+ φn(z)ψn(w) for some φ1, ψ1, …, φn, ψn: ℂ → ℂ. The rank of f with respect to g is defined as the minimum integer n for which such a decomposition is possible. It is proved that if g is an odd function, then the rank any function in F(g) is even.
About the authors
V. A. Bykovskii
Khabarovsk Branch of Institute of Applied Mathematics, Far East Branch
Author for correspondence.
Email: vab@iam.khv.ru
Russian Federation, ul. Dzerzhinskogo 54, Khabarovsk, 680000