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Operator Theory for Complex and Hypercomplex Analysis
Edited by: E. Ramírez de Arellano, Centro de Investigación y de Estudios Avanzados del IPN, Mexico, Mexico, N. Salinas, University of Kansas, Lawrence, KS, M. V. Shapiro, Instituto Politécnico Nacional, Mexico, Mexico, and N. L. Vasilevski, Centro de Investigación y de Estudios Avanzados del IPN, Mexico, Mexico

Contemporary Mathematics
1998; 298 pp; softcover
Volume: 212
ISBN-10: 0-8218-0677-7
ISBN-13: 978-0-8218-0677-7
List Price: US$83
Member Price: US$66.40
Order Code: CONM/212
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This book presents a collection of papers on certain aspects of general operator theory related to classes of important operators: singular integral, Toeplitz and Bergman operators, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure operator theory, and is influential and beneficial for important areas of analysis. Particular attention is paid to the fruitful interplay of recent developments of complex and hypercomplex analysis on one side and to operator theory on the other. The majority of papers illustrate this interplay as well as related applications. The papers represent the proceedings of the conference "Operator Theory for Complex and Hypercomplex Analysis", held in December 1994 in Mexico City.


Graduate students and research mathematicians interested in operator theory, analysis of one and several complex variables, hypercomplex analysis, functional analysis, mathematical physics and related areas.

Table of Contents

  • D. E. Barrett -- The Bergman projection on sectorial domains
  • R. Beals, B. Gaveau, and P. Greiner -- Subelliptic geometry
  • H. Begehr and G. N. Hile -- Higher order Cauchy Pompeiu operators
  • M. Cotlar and C. Sadosky -- A polydisk version of Beurling's characterization for invariant subspaces of finite multi-codimension
  • B. Fischer and N. Tarkhanov -- A representation of solutions with singularities
  • E. Franks and J. Ryan -- Bounded monogenic functions on unbounded domains
  • M. Gromov, G. Henkin, and M. Shubin -- \(L^2\) holomorphic functions on pseudo-convex coverings
  • K. Gürlebeck -- On some operators in Clifford analysis
  • U. Hagenbach and H. Upmeier -- Toeplitz \(C^*\)-algebras over non-convex cones and pseudo-symmetric spaces
  • A. M. Kytmanov and S. G. Myslivets -- On an application of the Bochner-Martinelli operator
  • N. K. Karapetyants -- Local estimates for fractional integral operators and potentials
  • C. Li and Z. Wu -- Hankel operators on Clifford valued Bergman space
  • M. Martin and N. Salinas -- Weitzenböck type formulas and joint seminormality
  • V. S. Rabinovich -- \(C^*\)-algebras of pseudodifferential operators and limit operators
  • E. R. de Arellano and N. Vasilevski -- Bargmann projection, three-valued functions and corresponding Toeplitz operators
  • R. M. Range -- Singular integral operators in the \(\bar{\partial}\) theory on convex domains in \(\mathbb{C}^n\)
  • S. G. Samko -- Differentiation and integration of variable order and the spaces \(L^{p(x)}\)
  • A. G. Sergeev -- Twistor quantization of loop spaces and general Kähler manifolds
  • M. Shapiro and L. M. Tovar -- On a class of integral representations related to the two-dimensional Helmholtz operator
  • M. M. Smirnov -- Cocycles on the gauge group and the algebra of Chern-Simons classes
  • W. Sprössig -- Boundary value problems treated with methods of Clifford analysis
  • F. H. Szafraniec -- Analytic models of the quantum harmonic oscillator
  • A. Turbiner -- Interesting relations in Fock space
  • A. Unterberger -- Quantization: Some problems, tools, and applications
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