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Journal of Soviet Mathematics

V norm) function Here E(t) is a J-nonnegative, J-nondecreasing, continuous (in the ,~with values in ~o(G); ~(t) is a scalar, nondecreasing, left-continuous function (0 ! t 5 i).The space of realizations X0 = Y0 consists of the functions g:[0, I] + G, for which 1 (g, g)xc = I (ddE (t) g(l), g (t))a < oo.0The pencil XA 0 + B 0 is a triangular model of the continuous component XA c + B c.The questions touched upon in Sec.6, 7 have been more completely presented in [8]; also there one discusses the applications of the results to the analysis and synthesis of control systems of the form (8) and to the investigation of the Cauchy problem for Eq.(8.1).lo 2. 4.. 6. 7.8.

Equations with a difference kernel on a system of intervals