Strongly bounded variation functions in Krein spaces

In the present paper, we introduce the notion of strongly bounded variation function in Krein spaces, we then show that the definition of bounded variation is independent of the decomposition of the Krein space, and the definition of bounded variation of a function in Hilbert spaces given in [V.V. Chistyakov, J. Dynam.Control Syst., 3 (1997), 261-289], is a particular case of the one introduced in this paper.We show a technique for constructing bounded variation functions on Krein spaces from bounded variation functions on the Hilbert subspaces composing the Krein space.