60 citations · 414 across the 46 of their papers we have counts for
4 papers · 2 filters
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…