On the basis property of root function systems of Dirac operators with regular boundary conditions (original) (raw)

where B is a nonsingular diagonal n× n matrix, B = diag(b−1 1 In1, . . . , b −1 r Inr) ∈ Cn×n, n = n1 + . . . nr, with complex entries bj 6= bk, and Q(x) is a potential matrix takes its origin in the paper by Birkho and Langer [4]. Afterwards their investigations were developed in many directions. Malamud and Oridoroga in [20] established rst general results on completeness of root function systems of boundary value problems for di erential systems (1). A little bit later Lunyov and Malamud in [17] obtained rst general results on Riesz basis property (Riesz basis property with parentheses) for mentioned boundary value problems with a potential matrix Q(x) ∈ L∞. There is an enormous literature related to the spectral theory outlined above, and we refer to [6, 7, 16, 22, 25] and their extensive reference lists for this activity. In the present paper, we study the Dirac system