On the basicity of derived chains

We introduce the definition of a derived chain, which generalizes the corresponding concept introduced by M. V. Keldysh and which corresponds, for example, to problems more general than the Cauchy problem. It is shown that subspaces consisting of derived chains form a Riesz basis. The class of derived chains considered includes those which correspond to certain boundary value problems on an infinite interval with the condition of convergence to zero of a vector-valued function, that depends on $t$, as $t\to\infty$. The operator-valued functions with respect to whose root vectors the derived chains are formed are similar to the Keldysh operator bundles.
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