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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 .
This book contains both expository articles and original research
in the areas of function theory and operator theory. The
contributions include extended versions of some of the lectures by
invited speakers at the conference in honor of the memory of
Serguei Shimorin at the Mittag-Leffler Institute in the summer of
2018. The book is intended for all researchers in the fields of
function theory, operator theory and complex analysis in one or
several variables. The expository articles reflecting the current
status of several well-established and very dynamical areas of
research will be accessible and useful to advanced graduate
students and young researchers in pure and applied mathematics, and
also to engineers and physicists using complex analysis methods in
their investigations.
This book contains both expository articles and original research
in the areas of function theory and operator theory. The
contributions include extended versions of some of the lectures by
invited speakers at the conference in honor of the memory of
Serguei Shimorin at the Mittag-Leffler Institute in the summer of
2018. The book is intended for all researchers in the fields of
function theory, operator theory and complex analysis in one or
several variables. The expository articles reflecting the current
status of several well-established and very dynamical areas of
research will be accessible and useful to advanced graduate
students and young researchers in pure and applied mathematics, and
also to engineers and physicists using complex analysis methods in
their investigations.
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