On the gaps in the spectrum associated with Hill’s equation
M. S. P. Eastham · Proceedings of the American Mathematical Society · 1969
inasmuch as that this condition automatically implies that ,u_ 0 for all gaps. Actually, Putnam worked with a=1, but the results for general a are obtained by the transformation x = at. In this paper I answer Putnam's question in the negative in ?2 by constructing a q(x) satisfying (1.3) such that the first gap in S has length exceeding (1.2). I mention here for comparison with (1.4) that my q(x) satisfies