Title: Eigenfunctions of Periodic Differential Operators Analytic in a Strip,
Abstract: Ordinary differential operators with periodic coefficients analytic in a
strip act on a Hardy-Hilbert space of analytic functions with inner product
defined by integration over a period on the boundary of the strip. Simple
examples show that eigenfunctions may form a complete set for a narrow strip,
but completeness may be lost for a wide strip. Completeness of the
eigenfunctions in the Hardy-Hilbert space is established for regular second
order operators with matrix-valued coefficients when the leading coefficient
satisfies a positive real part condition throughout the strip.