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Aleksandrov-Clark measures. (English) Zbl 1102.30032
Matheson, Alec L. (ed.) et al., Recent advances in operator-related function theory. Proceedings of the conference, Dublin, Ireland, August 4–6, 2004. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3925-X/pbk). Contemporary Mathematics 393, 1-14 (2006).
The authors introduce a family of unitary transformations discovered by D. N. Clark and present some of the results spawned by this basic discovery including a refinement of P. Fatou’s classical theorem on existence of nontangential boundary values, applications of AC (Aleksandrov-Clark) measures in the study of boundary behavior of Cauchy-Stieltjes integrals, perturbation theory, operator theory, composition operators, and in the Nehari interpolation problem. Also, a circle of ideas centered on the notion of a rigid function in the Hardy space \(H^1\) are discussed.
For the entire collection see [Zbl 1083.46001].

MSC:
30D55 \(H^p\)-classes (MSC2000)
30D50 Blaschke products, etc. (MSC2000)
30E05 Moment problems and interpolation problems in the complex plane
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
47A45 Canonical models for contractions and nonselfadjoint linear operators
47A55 Perturbation theory of linear operators
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47B33 Linear composition operators
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