Problems of Adamjan—Arov—Krein Type on Subsets of the Circle and Minimal Norm Extensions
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We constructively solve a pair of band-limited generalizations of the Adamjan—Arov—Krein problem. The first one consists in extending a function given on a proper subset of the unit circle to the whole circle so as to make it as close as possible to meromorphic with the prescribed number of poles, in the sup norm, while meeting some gauge constraint. The second consists in directly approximating the given function on the proper subset by the restriction of a meromorphic function, again meeting some gauge constraint.
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