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

James Adduci; Boris Mityagin

Open Mathematics (2012)

  • Volume: 10, Issue: 2, page 569-589
  • ISSN: 2391-5455

Abstract

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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).

How to cite

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James Adduci, and Boris Mityagin. "Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis." Open Mathematics 10.2 (2012): 569-589. <http://eudml.org/doc/269402>.

@article{JamesAdduci2012,
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).},
author = {James Adduci, Boris Mityagin},
journal = {Open Mathematics},
keywords = {Harmonic oscillator; Hermite functions; Discrete Hilbert transform; Unconditional basis; harmonic oscillator; discrete Hilbert transform; unconditional basis},
language = {eng},
number = {2},
pages = {569-589},
title = {Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis},
url = {http://eudml.org/doc/269402},
volume = {10},
year = {2012},
}

TY - JOUR
AU - James Adduci
AU - Boris Mityagin
TI - Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 569
EP - 589
AB - 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).
LA - eng
KW - Harmonic oscillator; Hermite functions; Discrete Hilbert transform; Unconditional basis; harmonic oscillator; discrete Hilbert transform; unconditional basis
UR - http://eudml.org/doc/269402
ER -

References

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