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A class of integral operators on spaces of analytic functions

Aleman, Alexandru LU (2007) In Topics in Complex Analysis and Operator Theory,Winter School in Complex Analysis and Operator Theory p.3-30
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Topics in Complex Analysis and Operator Theory,Winter School in Complex Analysis and Operator Theory
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3 - 30
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Universidad de Malaga, 2007.
language
English
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ABSTRACTS OF THE COURSES Winter School in Complex Analysis and Operator Theory Antequera, M´alaga, Spain. February 5-9, 2006 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− A CLASS OF INTEGRAL OPERATORS ON SPACES OF ANALYTIC FUNCTIONS Alexandru Aleman, Alexandru.Aleman@math.lu.se Lund University, Sweden Abstract The lectures will be concerned with integral operators of the form Tgf(z) = Z z 0 f(t)g0(t)dt where g is a fixed analytic function in the unit disc called symbol. These operators appear in a natural way in many problems in complex analysis and I plan to give a detailed account on some of these. We shall then discuss various basic properties of these operators acting between some common spaces of analytic functions on the disc, more precisely between Hardy and weighted Bergman spaces. Most known results about these operators characterize the symbols g such that Tg acts as a bounded, compact or Schatten-class operator between given spaces as above and I will present some of these. Finally, we shall turn to more specific questions like the spectrum and invariant subspaces for such operators. These problems turn out to be quite difficult in the general case and for this reason we shall restrict our attention to certain special cases which are of interest in their own right.
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ed111785-a915-4165-b2e8-85c3f1badd74 (old id 1467155)
date added to LUP
2016-04-04 09:59:48
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2018-11-21 20:56:06
@article{ed111785-a915-4165-b2e8-85c3f1badd74,
  author       = {Aleman, Alexandru},
  language     = {eng},
  pages        = {3--30},
  publisher    = {Universidad de Malaga, 2007.},
  series       = {Topics in Complex Analysis and Operator Theory,Winter School in Complex Analysis and Operator Theory},
  title        = {A class of integral operators on spaces of analytic functions},
  year         = {2007},
}