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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access January 18, 2012

Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis

  • James Adduci EMAIL logo and Boris Mityagin
From the journal Open Mathematics

Abstract

For any complex valued L p-function b(x), 2 ≤ p < ∞, or L ∞-function with the norm ‖b↾L ∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d 2/dx 2 + x 2 + b(x) in L 2(ℝ1) is discrete and eventually simple. Its SEAF (system of eigen- and associated functions) is an unconditional basis in L 2(ℝ).

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Published Online: 2012-1-18
Published in Print: 2012-4-1

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