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Equiconvergence theorems for singular Sturm-Liouville operators with various boundary conditions

Research paper by O. A. Shveikina

Indexed on: 22 Mar '15Published on: 22 Mar '15Published in: Differential Equations



Abstract

We consider the Sturm-Liouville operator L(y) = −d2y/dx2 + q(x)y in the space L2[0, π], where the potential q(x) is a complex-valued distribution of the first order of singularity; namely, q(x) = ut’(x), where u ∈ L2[0, π]. (The derivative is understood in the sense of distributions.) We study the uniform equiconvergence on the entire interval [0, π] of the expansions of a function f ∈ L2 in the system of eigenfunctions and associated functions of the operator L with the Fourier trigonometric series expansion. We also estimate the equiconvergence rate.