On an inequality of Kolmogorov type for a second-order difference expression
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Abstract
In this paper we discuss an inequality of Kolmogorov type for the square of a second-order formally symmetric difference expression in the limit-point case. A connection between the existence of the inequality and the Hellinger-Nevanlinna m(lambda) function associated with the difference expression is established and it is shown that the best constant in the inequality is determined by the behaviour of the m-function. Analytical and computational results are obtained for specific classes of problems. Also necessary and sufficient conditions for the powers of the difference expression to be partially separated are given.