Trace formulae and spectral inequalities for a class of differential operators

Muhammad Usman, Ari Laptev, COMSATS Institute Of Information Technology (Pakistan)
We study the scattering problem for the Schrodinger equation on the half-line with the Robin boundary condition at the origin. We derive an expression for trace of the difference of perturbed and unperturbed resolvent in terms of a Wronskian. This leads to a representation for the perturbation determinant and trace formulas of Buslaev-Faddeev type. We further generalize the method used for obtaining trace formulas to matrix-valued Schrodinger operator. We derive trace formulas for a star graph
more » ... hich satisfies Kirchhoff vertex condition at origin. Finally, we apply the commutation method to matrix-valued Schrodinger operator defined on the half-line with the Robin boundary condition at zero. We also obtain sharp Lieb-Thirring inequalities and show how they can be used for related problems.
doi:10.25560/14689 fatcat:4qz2v272dved7g7h7u3wspy2nq