Equiconvergence of spectral decompositions of Hill–Schrödinger operators

We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator L=−d2/dx2+v(x)L=−d2/dx2+v(x), x∈[0,π]x∈[0,π], with Hper−1-potential and the free operator L0=−d2/dx2L0=−d2/dx2, subject to periodic, antiperiodic or Dirichlet boundary conditions.In particular, we prove that‖SN−SN0:La→Lb‖→0if1