The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and sufficient condition) for the infinite dimensionality of its space $V_L$ of solutions belonging to R is the presence of a lacunary sequence in $V_L$.

翻译：摘要：引入了缺项无穷数值序列的概念。研究表明，对于任意系数属于无穷数值序列集R的线性差分算子L，其属于R的解空间$V_L$为无限维的充要条件（即必要且充分条件）是$V_L$中存在一个缺项序列。