Extremal Problems of Interpolation Theory

Abstract

We consider problems where one seeks m×m matrix valued H∞ functions w(ξ) which satisfy interpolation constraints and a bound (0.1) w∗(ξ)w(ξ) ≤ ρmin, |ξ| 0 where matrices X,R,C are N ×N matrices. When studying equation EXTREMAL PROBLEMS OF INTERPOLATION THEORY 821 (2.1) we apply the method of successive approximations. We put (2.2) X0 = R, Xn+1 = R + C∗X−1 n C. It follows from (2.2) that (2.3) Xn ≥ X0, n ≥ 0. As the righthand side of (2.1) decreases with the growth of X, then in view of (2.2) and (2.3) the inequalities (2.4) Xn ≤ X1, n ≥ 1 are true. Similarly we obtain that (2.5) Xn ≥ X2, n ≥ 2. This leads to the following assertion (found in [4, 5]).

Locations

• Rocky Mountain Journal of Mathematics - View - PDF