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1D dirac operators with special periodic potentials

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Djakov P., Mityagin B.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

tom 60

nr 1

59-75

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.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Djakov P.

1 Mityagin B.

1 2012

Wyniki wyszukiwania

1D dirac operators with special periodic potentials