TWO SEMINARS BY CONSTANZE LIAW (TAMU) ON FRIDAY, NOVEMBER 6


Mathematical Physics & Harmonic Analysis Seminar, 1:50, BLOC 627

'Singular Integral Operators and Rank One Perturbations'

The spectral representation of a self-adjoint rank one perturbation is 
given by a singular integral operator of special form. Such operators are 
connected with two weight estimates for the Cauchy transform. As an 
application, a sufficient condition for the perturbed operator to have 
purely absolutely continuous spectrum on a closed interval is given in 
terms of the density of the unperturbed operator's spectral measure.
(For those who have seen me speak about this topic previously, I am 
planning to emphasize regularizations of singular integral operators a 
little more.)


Linear Analysis Seminar, 4:00, MILN 317

'Unitary Rank One Perturbations and the Adjoint to the Clark Operator'

Although the Clark operator has been introduced over half a century ago, 
no complete representation formula has been published for its adjoint. 
However, partial representations have lead to important results in 
Spectral Theory using Harmonic and Complex Analysis; and vice versa. Using 
vector-valued Functional Models, we derive a complete representation for 
the adjoint to the Clark operator.