Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

this paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. it is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.

We discuss direct and inverse spectral theory of self-adjoint Sturm– Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl–Titchmarsh theory for these relations. Consequently, we apply de Branges’ subspace ordering theorem to obtain inverse uniqueness results for the associated spectral measure. The results can be applied to...

Based on high energy expansions and Herglotz properties of Green and Weyl m-functions we develop a self-contained theory of trace formulas for Jacobi operators. In addition, we consider connections with inverse spectral theory, in particular uniqueness results. As an application we work out a new approach to the inverse spectral problem of a class of reflectionless operators producing explicit ...