To question on embedding of reproducing kernel Hilbert spaces

In this work we obtain necessary and sufficient conditions for embedding of one reproducing kernel Hilbert space into another reproducing kernel Hilbert space. The paper is a continuation of works by the authors, in which the problem on coincidence or equivalence of two reproducing kernel Hilbert spaces was studied. An important role is played by the consistence condition of two complete systems of functions with some linear continuous operator introduced by the authors before. The obtained results are demonstrated by particular examples.