9 research outputs found
On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach
On properties of linear operators of certain classes in rigged spaces with indefinite metric
Finite-Codimensional Compressions of Symmetric and Self-Adjoint Linear Relations in Krein Spaces
Schur analysis in an indefinite setting
Schur analysis comprises topics like: the Schur transformation on the class of Schur functions (by definition, the functions which are holomorphic and bounded by 1 on the open unit disk) and the Schur algorithm, Schur parameters and approximation, interpolation problems for Schur functions, factorization of rational 2 × 2 matrix polynomials, which are -unitary on the unit circle, and a related inverse scattering problem. This note contains a survey of indefinite versions of these topics related to the class of scalar generalized Schur functions. These are the meromorphic functions s(z) on the open unit disk for which the kernel has finitely many negative squares. We also review a generalization of the Schur transformation to classes of functions on a general domain one of which is the class of scalar generalized Nevanlinna functions. These are the meromorphic functions n(z) on the open upper half plane for which the kernel has finitely many negative squares.</p