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- W2078174985 abstract "We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator L = − d 2 / d x 2 + v ( x ) , x ∈ [ 0 , π ] , with H per − 1 -potential and the free operator L 0 = − d 2 / d x 2 , subject to periodic, antiperiodic or Dirichlet boundary conditions. In particular, we prove that ‖ S N − S N 0 : L a → L b ‖ → 0 if 1 < a ⩽ b < ∞ , 1 / a − 1 / b < 1 / 2 , where S N and S N 0 are the N -th partial sums of the spectral decompositions of L and L 0 . Moreover, if v ∈ H − α with 1 / 2 < α < 1 and 1 a = 3 2 − α , then we obtain uniform equiconvergence: ‖ S N − S N 0 : L a → L ∞ ‖ → 0 as N → ∞ ." @default.
- W2078174985 created "2016-06-24" @default.
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- W2078174985 date "2013-11-01" @default.
- W2078174985 modified "2023-09-29" @default.
- W2078174985 title "Equiconvergence of spectral decompositions of Hill–Schrödinger operators" @default.
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- W2078174985 doi "https://doi.org/10.1016/j.jde.2013.07.030" @default.
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