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In this paper we introduce a generating vector-operator acting on the classof functions $L_2([a,a+2l])$. This operator produces (for arbitrarily fixed$[a,a+2l]$) infinite number of new generation $L_2$-systems. Every element ofthe mentioned systems depends on Riemann's zeta-function and on Jacob's ladder.

Jacob's ladders and vector operator producing new generations of $L_2$-orthogonal systems connected with the Riemann's $\zeta(\frac 12+it)$ function