Equiconvergence of spectral decompositions of Hill-Schrödinger operators

2011/10/31 by Djakov, Plamen, Mityagin, Boris
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1110.6696

Abstract

We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator L= -d²/dx² + v(x), x ∈ [0,π], with H_per^-1 -potential and the free operator L⁰=-d²/dx², subject to periodic, antiperiodic or Dirichlet boundary conditions. In particular, we prove that ‖S_N - S_N⁰: L^a → L^b ‖ → 0 if 1

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