Bari-Markus property for Riesz projections of Hill operators with singular potentials

2008/03/21 by Plamen Djakov, Djakov, Plamen, Boris Mityagin +1
Mathematics · #34L40 #47B06 #47E05 #Analytic and geometric function theory #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0803.3170

openalex publication_date 2008/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Hill operators L y = - y^{′ ′} + v(x) y, x ∈ [0,π], with H^-1 periodic potentials, considered with periodic, antiperiodic or Dirichlet boundary conditions, have discrete spectrum, and therefore, for sufficiently large N, the Riesz projections P_n = (1)/(2πi) ∫_Cn (z-L)^-1 dz, C_n=\z: |z-n²|= n\ are well defined. It is proved that ∑_ngt;N ‖P_n - P_n⁰‖²_HS lt; ∞, where P_n⁰ are the Riesz projection of the free operator and ‖⋅‖_HS is the Hilbert--Schmidt norm.

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