Spectral Characteristics of the Sturm-Liouville Operator under Minimal Restrictions on Smoothness of Coefficients

In this paper we consider the Sturm-Liouville problem in general form with Dirichlet boundary conditions under the minimal smoothness assumptions for the coefficients. We obtain the asymptotics formulas for eigenvalues and eigenfunctions of this problem. Under the assumption that the Lp-norm of eigenfunctions is equal to 1, we get uniform estimates of the Chebyshev norm.

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