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Studies on Composition Operators
Edited by: Farhad Jafari, University of Wyoming, Laramie, WY, Barbara D. MacCluer, University of Virginia, Charlottesville, VA, Carl C. Cowen, Purdue University, West Lafayette, IN, and A. Duane Porter, University of Wyoming, Laramie, WY
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Contemporary Mathematics
1998; 252 pp; softcover
Volume: 213
ISBN-10: 0-8218-0768-4
ISBN-13: 978-0-8218-0768-2
List Price: US$60
Member Price: US$48
Order Code: CONM/213
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This book reflects the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on "Composition Operators on Spaces of Analytic Functions" held at the University of Wyoming. The readers will find here a collection of high-quality research and expository articles on composition operators in one and several variables. The book highlights open questions and new advances in the classical areas and promotes topics which are left largely untreated in the existing texts.

In the past two decades, the study of composition operators has experienced tremendous growth. Many connections between the study of these operators on various function spaces and other branches of analysis have been established. Advances in establishing criteria for membership in different operator classes have led to progress in the study of the spectra, adjoints, and iterates of these operators. More recently, connections between these operators and the study of the invariant subspace problem, functional equations, and dynamical systems have been exploited.

Readership

Graduate students and research mathematicians interested in operator theory, electrical engineers working in control theory, and physicists working on hyperbolic manifolds.

Table of Contents

  • P. S. Bourdon -- Convergence of the Koenigs sequence
  • B. A. Cload -- Generating the commutant of a composition operator
  • C. C. Cowen and B. D. MacCluer -- Some problems on composition operators
  • T. Domenig -- Order bounded and \(p\)-summing composition operators
  • H. Heidler -- Algebraic and essentially algebraic composition operators on the ball or polydisk
  • R. A. Hibschweiler -- Composition operators on spaces of Cauchy transforms
  • W. E. Hornor and J. E. Jamison -- Isometrically equivalent composition operators
  • T. L. Kriete III -- Kernel functions and composition operators in weighted Bergman spaces
  • B. A. Lotto -- A compact composition operator that is not Hilbert-Schmidt
  • J. S. Manhas -- Weighted composition operators on weighted spaces of continuous functions
  • V. Matache -- The eigenfunctions of a certain composition operator
  • P. R. Mercer -- Composition operators over convex domains in \(\mathbb{C}^n\)
  • I. Mihaila -- Composition operators on Riemann surfaces
  • A. Montes-Rodríguez -- Composition operators and hypercyclic vectors
  • P. Poggi-Corradini -- The essential norm of composition operators revisited
  • M. E. Robbins -- Composition operators between Bergman spaces
  • B. Russo -- Holomorphic composition operators in several complex variables
  • J. H. Shapiro -- Composition operators and Schröder's functional equation
  • A. G. Siskakis -- Semigroups of composition operators on spaces of analytic functions, a review
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