2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58453Foundations of the theory of Hilbert spaces with reproducing kernels are discussed. It is demonstrated that the claims in the papers of S.Saitoh and in his book "Theory of reproducing kernels and applications, Pitman research notes, 189, Longman, New York, 1988, that a characterization of the range of arbitrary linear transform is obtained in his works, is not correct.Mathematical PhysicsFunctional Analysis47B25text