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

• Autorzy: James Adduci , Boris Mityagin
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

Harmonic oscillator; Hermite functions; Discrete Hilbert transform; Unconditional basis

Kategorie tematyczne

• 34L10: Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions
• 47E05: Ordinary differential operators (should also be assigned at least one other classification number in section 47)
• 34L40: Particular operators (Dirac, one-dimensional Schr\"odinger, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 569-589

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

James Adduci

• The Ohio State University

autor

Boris Mityagin

• The Ohio State University

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Identyfikatory

DOI

10.2478/s11533-011-0139-3