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The goal of this paper is to solve the Caratheodory interpolation problem in the class  R q  [ a,b ] of matrix-functions with the help of the V. P. Potapov´s fundamental matrix Inequality method. In the completely indeterminate case, the general solution is described in terms of a linear fractional transformation.

The completely indeterminate Caratheodory matrix problem in the R q [ a , b ] class