On solvability of linear difference equations in smooth and real analytic vector functions of several variables

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Abstract

We investigate the multidimensional equations ∑j=1q Aj(x)y(x+ej)=f(x), ej ∈ ℝn where x ∈ ℝn and Aj : ℝn →Hom(ℝp,ℝm), f : ℝn → ℝm are given maps. Sufficient conditions for smooth and analytic solvability for any f ∈ Ck, k ≤ ω are found.

Original languageEnglish
Pages (from-to)123-129
Number of pages7
JournalIntegral Equations and Operator Theory
Volume18
Issue number2
DOIs
StatePublished - 1 Jun 1994

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