On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

Lieb–Thirring inequalities for an effective Hamiltonian of bilayer graphene

“…Laptev, and Safronov [23], Fanelli, Krejčiřík, and Vega [15] and [16], Mizutani [40], Fanelli and Krejčiřík [17], Cuenin and Kenig [10], and Lee and Seo [38], dealing with spectral properties of complex Schrödinger operators. Similar problems for Dirac, fractional Schrödinger and other types of operators were treated in Cuenin, Laptev, and Tretter [8], Cuenin and Seigl [9], Dubuisson [14], Cuenin [6] and [11], Cossetti [12], Ibrogimov, Krejčiřík, and Laptev [34], and Hulko [30] and [31]. A series of results on spectral analysis of Jacobi matrices can be found in Borichev, Golinskii, and Kupin [4] and [5] and Golinskii and Kupin [26]- [29].…”

Lieb-Thirring inequalities for an effective Hamiltonian of bilayer graphene

“…Among relatively recent papers in this direction, we quote articles by Demuth-Hansmann-Katriel [13], Frank [19], [20], Frank-Simon [22], Frank-Sabin [21], Frank-Laptev-Safronov [23], Fanelli-Krejčiřík-Vega [15,16], Mizutani [40], Fanelli-Krejčiřík [17], Cuenin-Kenig [10] and Lee-Seo [38], dealing with spectral properties of complex Schrödinger operators. Similar problems for Dirac, fractional Schrödinger and other types of operators were treated in Cuenin-Laptev-Tretter [8], Cuenin-Seigl [9], Dubuisson [14], Cuenin [6,11], Cossetti [12], Ibrogimov-Krejčiřík-Laptev [34] and Hulko [30,31]. A series of results on spectral analysis of Jacobi matrices can be found in Borichev-Golinskii-Kupin [4,5] and Golinskii-Kupin [26]- [29].…”

Location of eigenvalues of non-self-adjoint discrete Dirac operators

“…For the fusion (α)∩(γ) in the continuous setting, see [9,7,12,29,13,8,10,14]. For the complete combination (α)∩(β)∩(γ), we are only aware of the works [3,24] concerned with estimates on the number of discrete eigenvalues.…”