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  • Research Article
  • Open Access

Compact Weighted Composition Operators and Fixed Points in Convex Domains

Fixed Point Theory and Applications20072007:028750

  • Received: 18 April 2007
  • Accepted: 24 June 2007
  • Published:


Let be a bounded, convex domain in , and suppose that is holomorphic. Assume that is analytic, bounded away from zero toward the boundary of , and not identically zero on the fixed point set of . Suppose also that the weighted composition operator given by is compact on a holomorphic, functional Hilbert space (containing the polynomial functions densely) on with reproducing kernel satisfying as . We extend the results of J. Caughran/H. Schwartz for unweighted composition operators on the Hardy space of the unit disk and B. MacCluer on the ball by showing that has a unique fixed point in . We apply this result by making a reasonable conjecture about the spectrum of based on previous results.


  • Differential Geometry
  • Composition Operator
  • Computational Biology
  • Convex Domain
  • Weight Composition


Authors’ Affiliations

Department of Mathematics, University of California, Riverside, CA 92521, USA


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