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Difference equations in weighted spaces of sequences
Let $\varphi= \{\varphi_m\}_{m=1}^{\infty}$ be a family of convex functions $\varphi_m$ on ${\mathbb R}^n$ with certain growth conditions. With a help of restrictions of functions $\varphi_m$ on ${\mathbb Z}^n$ a weighted space of functions on ${\mathbb Z}^n$ denoted as $A_{\varphi}$ is defined. Linear continuous functionals on this space in terms of …