Some strong limit-2 and Dirichiet criteria for fourth order differential expressions

Abstract

AbstractConditions are given on the real coefficients p, q and r and the weight w, for the fourth order formally symmetric differential expressionto have the properties of being strong limit-2 and Dirichlet at ∞, when considered in the weighted Hilbert space, . These extend existing results due to both W. N. Everitt and V. Krishna Kumar and cover an expression which is important in the study of certain orthogonal polynomials.