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QA331. FCT 96915 Taylor coefficients and coefficient multipliers of Hardy and Bergman-type spaces | QA331.SPR FCT 103602 Harmonic quasiconformal mappings and hyperbolic type metrics | QA331.SPR FCT 81188 Vitushkin’s conjecture for removable sets | QA331.SPR FCT 81674 The hardy space of a slit domain | QA331.SPR FCT 81688 Arrangements, local systems and singularities | QA331.SPR FCT 81756 Complex Kleinian groups | QA331.SPR FCT 81831 Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory |
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If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .
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