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On Lieb-Thirring inequalities for multidimensional Schrödinger operators with complex potentials
Sabine Bögli, Sukrid Petpradittha, František Štampach
We solve the open problem by Demuth, Hansmann, and Katriel announced in [Integr. Equ. Oper. Theory 75 (2013), 1-5] by a counter-example construction. The problem concerns a possibl…
On the ground state of lattice Schrödinger operators
Michal Jex, František Štampach
We prove necessary and sufficient conditions for lattice Schrödinger operators to have a zero energy bound state in arbitrary dimension. The two criteria are sharp, complementary,…
Criticality transition for positive powers of the discrete Laplacian on the half line
Borbala Gerhat, David Krejcirik, Frantisek Stampach
We study the criticality and subcriticality of powers with of the discrete Laplacian acting on . We prove that these positive powers of the…
New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials
František Štampach, Pavel Šťovíček
Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter are presented. The Hankel matrices are regarded as matrix operators on the Hilbe…
Location of eigenvalues of non-self-adjoint discrete Dirac operators
Biagio Cassano, Orif O. Ibrogimov, David Krejcirik +1
We provide quantitative estimates on the location of eigenvalues of one-dimensional discrete Dirac operators with complex -potentials for . As a corollar…
Spectral enclosures for non-self-adjoint discrete Schrödinger operators
Orif O. Ibrogimov, František Štampach
We study location of eigenvalues of one-dimensional discrete Schrödinger operators with complex -potentials for . In the case of -potentials…