Polynomial-like elements in vector spaces with group actions

2018/08/09 by Minh Kha, Kha, Minh, Vladimir Lin +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1808.03366

openalex publication_date 2018/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study polynomial-like elements in vector spaces equipped with group actions. We first define these elements via iterated difference operators. In the case of a full rank lattice acting on an Euclidean space, these polynomial-like elements are exactly polynomials with periodic coefficients, which are closely related to solutions of periodic differential equations. Our main theorem confirms that if the space of polynomial-like elements of degree zero is of finite dimension then for any n ∈ ℤ₊, the space consisting of all polynomial-like elements of degree at most n is also finite dimensional.

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