Dirac system with potential lying in Besov spacesстатья
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Дата последнего поиска статьи во внешних источниках: 19 июля 2016 г.
Аннотация:We study the spectral properties of the Dirac operator L_{P,U} generated in the space (L_2[0, π])2 by the differential expression By′ + P(x)y and by Birkhoff regular boundary conditions U, where y = (y_1, y_2)^t , B=(−i 0 \\ 0 i), and the entries of the matrix P are complexvalued Lebesgue measurable functions on [0, π]. We also study the asymptotic properties of the eigenvalues {λ_n}, n∈Z, of the operator L_{P,U} as n → ∞ depending on the “smoothness” degree of the potential P; i.e., we consider the scale of Besov spaces B_{1,∞}^θ , θ ∈ (0,1). In the case of strongly regular boundary conditions, we study the asymptotic behavior of the system of normalized eigenfunctions of the operator L_{P,U} , and in the case of regular but not strongly regular boundary conditions, we find the asymptotics of two-dimensional spectral projections.