On the question of the coincidence of Hilbert spaces square-integrable with respect to the measure of functions

The problem of coincidence (equivalence) of two Hilbert spaces with a reproducing core. In some Hilbert space H, two complete systems in H are space generation of H and H it is required to find conditions under which the spaces H and H consist of the same functions, and at the same time the norms of functions in these spaces are equal (eqvivalent), i.e. H and H coincide (equivalent). In addition, in the work it is proved that when the complete the systems are orthosimilar in the space H with different measures, then the spaces H and H do not coincide. The problem of the coincidence (equivalence) of the spaces of restrictions of functions from Hilbert spaces with the reproducing kernel is also considered.