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

Genrich Belitskii; Vadim Tkachenko

doi:10.1007/BF01192455

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

Genrich Belitskii
, Vadim Tkachenko

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We investigate the multidimensional equations ∑_j=1^q A_j(x)y(x+e_j)=f(x), e_j ∈ ℝⁿ where x ∈ ℝⁿ and A_j : ℝⁿ →Hom(ℝ^p,ℝ^m), f : ℝⁿ → ℝ^m are given maps. Sufficient conditions for smooth and analytic solvability for any f ∈ C^k, k ≤ ω are found.

Original language	English
Pages (from-to)	123-129
Number of pages	7
Journal	Integral Equations and Operator Theory
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/BF01192455
State	Published - 1 Jun 1994

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/BF01192455

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title = "On solvability of linear difference equations in smooth and real analytic vector functions of several variables",

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.",

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year = "1994",

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T1 - On solvability of linear difference equations in smooth and real analytic vector functions of several variables

AU - Belitskii, Genrich

AU - Tkachenko, Vadim

PY - 1994/6/1

Y1 - 1994/6/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0002348127

U2 - 10.1007/BF01192455

DO - 10.1007/BF01192455

M3 - Article

AN - SCOPUS:0002348127

SN - 0378-620X

VL - 18

SP - 123

EP - 129

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

ER -

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

Abstract

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