Fréchet-valued formal power series

2019/01/12 by Thai Thuan Quang, Quang, Thai Thuan
Mathematics · #16W60 #31C10 #32A10 #46E50 #46G20 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1901.03825

openalex publication_date 2019/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a non-projectively-pluripolar set in a Fréchet space E. We give sufficient conditions to ensure the convergence on some zero-neighbourhood in E of a (sequence of) formal power series of Fréchet-valued continuous homogeneous polynomials provided that the convergence holds at a zero-neighbourhood of each complex line ℓ_a := \C a for every a ∈ A.

Related

• On Convergence Sets of Formal Power Series
• Topology and geometry of the general composition of formal power series -- towards Fréchet-Lie group-like formalism
• Pluripolar hulls and convergence sets
• A quantitative Khintchine-Groshev type theorem over a field of formal series
• The convergence of a sequence of polynomials and the distribution of their zeros