A CHARACTERIZATION OF THE SPECTRUM OF HILL'S OPERATOR

This article contains a complete derivation of necessary and sufficient conditions which a given sequence of intervals must satisfy in order that a Hill differential operator , with real, periodic potential , exist, whose spectrum coincides with this sequence of intervals. The proof is based on a specific representation of entire functions such that the equation has only real roots, conformal mappings having properties associated with this representation, and refined asymptotic formulas for the eigenvalues of certain boundary value problems.Bibliography: 17 titles.

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