Relations between limit-point and Dirichlet properties of second-order difference operators
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Abstract
We consider second-order difference expressions, with complex coefficients, of the form w(n)(-1)[-Delta(p(n-1)Delta x(n-1)) + q(n)x(n)] acting on infinite sequences. The discrete analog of some known relationships in the theory of differential operators such as Dirichlet, conditional Dirichlet, weak Dirichlet, and strong limit-point is considered. Also, connections and some relationships between these properties have been established.