Showing papers by "Albrecht Böttcher published in 2017"

Exploration of Toeplitz-like matrices with unbounded symbols is not a purely academic journey

Abstract: Exploration of Toeplitz-like matrices with unbounded symbols is not a purely academic journey

Similarity Between Two Projections

Abstract: Given two orthogonal projections P and Q, we are interested in all unitary operators U such that UP=QU and UQ=PU. Such unitaries U have previously been constructed by Wang, Du, and Dou and also by one of the authors. One purpose of this note is to compare these constructions. Very recently, Dou, Shi, Cui, and Du described all unitaries U with the required property. Their proof is via the two projections theorem by Halmos. We here give a proof based on the supersymmetric approach by Avron, Seiler, and one of the authors.

The Duduchava–Roch Formula

Abstract: The Duduchava–Roch formula is a formula for the inverse of a Toeplitz matrix that is generated by a pure Fisher–Hartwig singularity. We cite this formula with a full proof and give several of its applications. These are the Fredholm theory of Toeplitz operators with piecewise continuous symbols, the derivation of the pure Fisher–Hartwig determinant, problems connected with lattice determinants, and Green’s function for a boundary value problem for a higher-order ordinary differential operator.