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The simplest representations of triangular parts of fmite rank kernels are analysed. Criteria for uniqueness up to similarity are given. The results are applied to the problem of minimal realization of systems with separable boundary conditions. V 1987 Academx Press. Inc (0.2) Here for v = 1, 2 the functions F"( . ) and G,( .) are matrix functions of sizes m x n, and n, x m, respectively, and their entries are square integrable on [a, b]. In LT[a, b], Eq. (0.1) is equivalent to the following two point boundary value problem: 436doi:10.1016/0022-247x(87)90007-2 fatcat:sybio4s7zraw3hppsrbbk6y4ia