Abstract:
The Sturm-Liouville operator $L=-d^2/dx^2+q(x)$ in the space $L_2[0,\pi]$ under Dirichlet boundary conditions is investigated. It is assumed that $q(x)=u'(x)$, $u(x)\in L_2[0,\pi]$ (here, differentiation is used in the distributional sense). The problem of when the expansion of a function $f(x)$ in terms of a series of eigenfunctions and associated functions of the operator $L$ is uniformly equiconvergent on the whole of the interval $[0,\pi]$ with its Fourier sine series expansion is considered. It is shown that such uniform convergence holds for any function $f(x)$ in the space $L_2[0,\pi]$.
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