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.
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978-0-8218-0677-7 (9780821806777)
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Schweitzer Klassifikation
The Bergman projection on sectorial domains by D. E. Barrett Subelliptic geometry by R. Beals, B. Gaveau, and P. Greiner Higher order Cauchy Pompeiu operators by H. Begehr and G. N. Hile A polydisk version of Beurling's characterization for invariant subspaces of finite multi-codimension by M. Cotlar and C. Sadosky A representation of solutions with singularities by B. Fischer and N. Tarkhanov Bounded monogenic functions on unbounded domains by E. Franks and J. Ryan $L^2$ holomorphic functions on pseudo-convex coverings by M. Gromov, G. Henkin, and M. Shubin On some operators in Clifford analysis by K. Gurlebeck Toeplitz $\textnormal{C}^*$-algebras over non-convex cones and pseudo-symmetric spaces by U. Hagenbach and H. Upmeier On an application of the Bochner-Martinelli operator by A. M. Kytmanov and S. G. Myslivets Local estimates for fractional integral operators and potentials by N. K. Karapetyants Hankel operators on Clifford valued Bergman space by C. Li and Z. Wu Weitzenbock type formulas and joint seminormality by M. Martin and N. Salinas $C^*$-algebras of pseudodifferential operators and limit operators by V. S. Rabinovich Bargmann projection, three-valued functions and corresponding Toeplitz operators by E. R. de Arellano and N. Vasilevski Singular integral operators in the $\bar{\partial}$ theory on convex domains in $\mathbb{C}^n$ by R. M. Range Differentiation and integration of variable order and the spaces $L^{p(x)}$ by S. G. Samko Twistor quantization of loop spaces and general Kahler manifolds by A. G. Sergeev On a class of integral representations related to the two-dimensional Helmholtz operator by M. Shapiro and L. M. Tovar Cocycles on the gauge group and the algebra of Chern-Simons classes by M. M. Smirnov Boundary value problems treated with methods of Clifford analysis by W. Sprossig Analytic models of the quantum harmonic oscillator by F. H. Szafraniec Interesting relations in Fock space by A. Turbiner Quantization: Some problems, tools, and applications by A. Unterberger.
