The Hardy Space of a Slit Domain by Alexandru Aleman

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  • Title: The Hardy Space of a Slit Domain
  • Author: Alexandru Aleman
  • Category: Mathematics
  • Date: January 2010
  • Lenguage: English
  • Pages: unknown
  • ISBN: 3034600984

 

Ebook description:

If H is a Hilbert area and T : H ? H is a continous linear operator, a pure query to ask is: What are the closed subspaces M of H for which T M ? M? Of course the well-known invariant subspace downside asks whether or not or not T has any non-trivial invariant subspaces. This monograph is a component of a lengthy line of examine of the invariant subspaces of the operator T = M (multiplication by the impartial variable z, i. e. , M f = zf )on a z z Hilbert area of analytic features on a bounded area G in C. The characterization of these M -invariant subspaces is especially fascinating because it entails each the properties z of the features contained in the area G, their zero units for instance, in addition to the conduct of the features close to the boundary of G. The operator M is just not solely fascinating in its z personal proper however usually serves as a mannequin operator for sure lessons of linear operators. By this we imply that given an operator T on H with sure properties (sure subnormal operators or two-isometric operators with the appropriate spectral properties, and so on. ), there’s a Hilbert area of analytic features on a area G for which T is unitarity equal to M

 

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