Linear Functional Equations and their Solutions in Lorentz Spaces

2021/01/07 by Janusz Morawiec, Morawiec, Janusz, Thomas Zürcher +1
Mathematics · #39B12 #47A50 (Primary) 26A24 #47B38 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical and Theoretical Analysis #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2101.02428

openalex publication_date 2021/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Assume that Ω⊂ ℝ^k is an open set, V is a separable Banach space over a field \mathbb K∈\\mathbb R,\mathbb C\ and f₁,…,f_N \colonΩ→ Ω, g₁,…, g_N\colonΩ→ \mathbbK, h₀\colon Ω→ V are given functions. We are interested in the existence and uniqueness of solutions φ\colon Ω→ V of the linear functional equation φ=∑_k=1^Ng_k⋅(φ∘ f_k)+h₀ in Lorentz spaces.

Related

• On a class of linear functional equations without range condition
• Some Class of Linear Operators Involved in Functional Equations
• Partial generalizations of some Conjectures in locally symmetric Lorentz spaces
• Anisotropic Grand Lorentz Spaces
• A note on invariant subspaces and the solution of some classical functional equations