**Contemporary Mathematics**

Volume: 212;
1998;
298 pp;
Softcover

MSC: Primary 47;
Secondary 30; 32

Print ISBN: 978-0-8218-0677-7

Product Code: CONM/212

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

**Electronic ISBN: 978-0-8218-7804-0
Product Code: CONM/212.E**

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

# Operator Theory for Complex and Hypercomplex Analysis

Share this page *Edited by *
*E. Ramírez de Arellano; N. Salinas; M. V. Shapiro; N. L. Vasilevski*

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.

#### Readership

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

## Operator Theory for Complex and Hypercomplex Analysis

- Contents vii8 free
- Preface ix10 free
- The Bergman projection on sectorial domains 112 free
- Subelliptic geometry 2536
- Higher order Cauchy Pompeiu operators 4152
- A polydisk version of Beurling's characterization for invariant sub-spacesof finite multi-codimension 5162
- A representation of solutions with singularities 5768
- Bounded monogenic functions on unbounded domains 7182
- L2 holomorphic functions on pseudo-convex coverings 8192
- On some operators in Clifford analysis 95106
- Toeplitz C*-algebras over non-convex cones and pseudo-sym-metric spaces 109120
- On an application of the Bochner-Martinelli operator 133144
- Local estimates for fractional integral operators and potentials 137148
- Hankel operators on Clifford valued Bergman space 143154
- Weitzenböck type formulas and joint seminormality 157168
- C*-algebras of pseudodifferential operators and limit operators 169180
- Bargmann projection, three-valued functions and corresponding Toeplitz operators 185196
- Singular integral operators in the ∂ theory on convex domains in Cn 197208
- Differentiation and integration of variable order and the spaces Lp(x) 203214
- Twistor quantization of loop spaces and general Kähler manifolds 221232
- On a class of integral representations related to the two-dimensional Helmholtz operator 229240
- Cocycles on the gauge group and the algebra of Chern-Simons classes 245256
- Boundary value problems treated with methods of Clifford analysis 255266
- Analytic models of the quantum harmonic oscillator 269280
- Interesting relations in Fock space 277288
- Quantization: Some problems, tools, and applications 285296