1D dirac operators with special periodic potentials

• Autorzy: Plamen Djakov , Boris Mityagin
• Języki publikacji: EN

Abstrakty

EN

For one-dimensional Dirac operators of the form
$Ly = i\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} dy/dx + vy$, $v = \begin{pmatrix) 0& Q\\ P & 0\end{pmatrix}$, $y = \begin{pmatrix}y₁\\y₂\end{pmatrix}$, x ∈ ℝ,
we single out and study a class X of π-periodic potentials v whose smoothness is determined only by the rate of decay of the related spectral gaps γₙ = |λ⁺ₙ - λ¯ₙ|, where $λₙ^{±}$ are the eigenvalues of L = L(v) considered on [0,π] with periodic (for even n) or antiperiodic (for odd n) boundary conditions.

Kategorie tematyczne

• 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: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: 60
• Numer: 1
• Strony: 59-75

Daty

wydano

2012

Twórcy

autor

Plamen Djakov

• Sabanci University, Orhanli, 34956 Tuzla, Istanbul, Turkey

autor

Boris Mityagin

• Department of Mathematics, The Ohio State University, 231 West 18th Ave., Columbus, OH 43210, U.S.A.

Identyfikatory

DOI

10.4064/ba60-1-5