Abstract
Methods of analyzing linear time-optimal control problems are adapted to the analysis of the extremal problem ∥ L| 0∥ ∞ = inf | ϵU ∥ L|∥ ∞; L is a linear nth order differential operator and U is a flat in the Sobolev space W n,∞ [ a, b]. Existence and uniqueness of solutions are established for particular U determined by interpolation conditions at a and b. Solutions are characterized as perfect splines, enabling one to obtain solutions of perfect-spline interpolation problems. Further, existence of perfect-spline solutions is established for extremal and interpolation problems determined by more general flats U.
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