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A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter

Abstract

We establish a criterion for a set of eigenfunctions of the one-dimensional Schrödinger operator with distributional potentials and boundary conditions containing the eigenvalue parameter to be a Riesz basis for \({\mathscr {L}}_2(0,\pi )\).

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Correspondence to Namig J. Guliyev.

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Guliyev, N.J. A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter. Anal.Math.Phys. 10, 2 (2020). https://doi.org/10.1007/s13324-019-00348-0

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Keywords

  • Riesz basis
  • One-dimensional Schrödinger equation
  • Distributional potential
  • Sturm–Liouville operator
  • Singular potential
  • Boundary conditions dependent on the eigenvalue parameter

Mathematics Subject Classification

  • 42C15
  • 42C30
  • 15B05
  • 34B07
  • 34L10
  • 34L40
  • 46B15
  • 46C05
  • 46E30
  • 47A20
  • 47B25
  • 47E05