60 citations · 414 across the 46 of their papers we have counts for
12 papers · 1 filter
Perspectives on General Left-Definite Theory
Dale Frymark, Constanze Liaw
In 2002, Littlejohn and Wellman developed a celebrated general left-definite theory for semi-bounded self-adjoint operators with many applications to differential operators. The th…
Preservation of absolutely continuous spectrum for contractive operators
Sergei Treil, Constanze Liaw
We consider contractive operators that are trace class perturbations of a unitary operator . We prove that the dimension functions of the absolutely continuous spectrum of $…
Dimension of the exceptional set in the Aronszajn-Donoghue theorem for finite rank perturbations
Constanze Liaw, Sergei Treil, Alexander Volberg
The classical Aronszajn-Donoghue theorem states that for a rank one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the…
Matrix-valued Aleksandrov--Clark measures and Carathéodory angular derivatives
Constanze Liaw, Robert T. W. Martin, Sergei Treil
This paper deals with families of matrix-valued Aleksandrov--Clark measures , corresponding to purely contractive matrix functi…
General Clark model for finite rank perturbations
Constanze Liaw, Sergei Treil
All unitary perturbations of a given unitary operator by finite rank operators with fixed range can be parametrized by unitary matrices ; this generalizes…
Singular integrals, rank one perturbations and Clark model in general situation
Constanze Liaw, Sergei Treil
We start with considering rank one self-adjoint perturbations with cyclic vector on a separable Hilbert space . The spectral…
Cyclic polynomials in two variables
Catherine Bénéteau, Greg Knese, Łukasz Kosiński +3
We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, whi…
Cyclicity in Dirichlet-type spaces and extremal polynomials II: functions on the bidisk
Catherine Bénéteau, Alberto A. Condori, Constanze Liaw +2
We study Dirichlet-type spaces of analytic functions in the unit bidisk and their cyclic elements. These are the functions for which there exists a sequence $(…
Clark model in general situation
Constanze Liaw, Sergei Treil
For a unitary operator the family of its unitary perturbations by rank one operators with fixed range is parametrized by a complex parameter . Namely all such unitary per…
A geometric approach to finite rank unitary perturbations
Ronald G. Douglas, Constanze Liaw
For a fixed natural number n, we consider a family of rank n unitary perturbations of a completely non-unitary contraction (cnu) with deficiency indices (n,n) on a separable Hilber…
Rank one perturbations and Anderson-type Hamiltonians
Constanze Liaw
Motivated by applications of the discrete random Schrödinger operator, mathematical physicists and analysts, began studying more general Anderson-type Hamiltonians; that is, the fa…
Rank one perturbations and singular integral operators
Constanze Liaw, Sergei Treil
We consider rank one perturbations of a self-adjoint operator with cyclic vector on a Hilbert space . The spectral repr…