This paper is concerned with the problem of characterizing those functions of minimum Lᵖ-norm on their nth derivative, 1 p ∞, that sequentially take on the given values (eᵢ )₁N. For p = ∞ the unique minimizing function is characterized. For p < ∞ fairly explicit necessary conditions are given.
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Allan M. Pinkus (1988) studied this question.