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2.—Semi-bounded Second-order Differential Operators

Synopsis Differential operators generated by the differential expression My(x) = —y″(x)+q(x)y(x) in L2(0, ∞) are considered. It is assumed that is bounded for all x in [0, ∞) and some fixed ω > 0. The operators are shown to be bounded below and an estimate for the lower bound is obtained in terms of q(x). In the case where q(x) is LP (0, ∞) for some p ≧ 1, the results are compared with recent ones of W. N. Everitt. Some comments are made on the best-possible nature of the results.