eBook ISBN:  9780821878040 
Product Code:  CONM/212.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821878040 
Product Code:  CONM/212.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 212; 1998; 298 ppMSC: Primary 47; Secondary 30; 32
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.
ReadershipGraduate 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

Articles

David E. Barrett — The Bergman projection on sectorial domains [ MR 1486586 ]

Richard Beals, Bernard Gaveau and Peter Greiner — Subelliptic geometry [ MR 1486587 ]

Heinrich Begehr and Gerald N. Hile — Higher order Cauchy Pompeiu operators [ MR 1486588 ]

Mischa Cotlar and Cora Sadosky — A polydisk version of Beurling’s characterization for invariant subspaces of finite multicodimension [ MR 1486589 ]

Bert Fischer and Nikolai Tarkhanov — A representation of solutions with singularities [ MR 1486590 ]

Edwin Franks and John Ryan — Bounded monogenic functions on unbounded domains [ MR 1486591 ]

M. Gromov, G. Henkin and M. Shubin — $L^2$ holomorphic functions on pseudoconvex coverings [ MR 1486592 ]

Klaus Gürlebeck — On some operators in Clifford analysis [ MR 1486593 ]

U. Hagenbach and H. Upmeier — Toeplitz $C^*$algebras over nonconvex cones and pseudosymmetric spaces [ MR 1486594 ]

A. M. Kytmanov and S. G. Myslivets — On an application of the BochnerMartinelli operator [ MR 1486595 ]

N. K. Karapetyants — Local estimates for fractional integral operators and potentials [ MR 1486596 ]

Chun Li and Zhijian Wu — Hankel operators on Clifford valued Bergman space [ MR 1486597 ]

Mircea Martin and Norberto Salinas — Weitzenböck type formulas and joint seminormality [ MR 1486598 ]

V. S. Rabinovich — $C^*$algebras of pseudodifferential operators and limit operators [ MR 1486599 ]

Enrique Ramírez de Arellano and Nikolai Vasilevski — Bargmann projection, threevalued functions and corresponding Toeplitz operators [ MR 1486600 ]

R. Michael Range — Singular integral operators in the $\overline \partial $ theory on convex domains in ${\bf C}^n$ [ MR 1486601 ]

Stefan G. Samko — Differentiation and integration of variable order and the spaces $L^{p(x)}$ [ MR 1486602 ]

A. G. Sergeev — Twistor quantization of loop spaces and general Kähler manifolds [ MR 1486603 ]

Michael Shapiro and Luis Manuel Tovar — On a class of integral representations related to the twodimensional Helmholtz operator [ MR 1486604 ]

M. M. Smirnov — Cocycles on the gauge group and the algebra of ChernSimons classes [ MR 1486605 ]

Wolfgang Sprössig — Boundary value problems treated with methods of Clifford analysis [ MR 1486606 ]

Franciszek Hugon Szafraniec — Analytic models of the quantum harmonic oscillator [ MR 1486607 ]

Alexander Turbiner — Interesting relations in Fock space [ MR 1486608 ]

André Unterberger — Quantization: some problems, tools, and applications [ MR 1486609 ]


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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.

Articles

David E. Barrett — The Bergman projection on sectorial domains [ MR 1486586 ]

Richard Beals, Bernard Gaveau and Peter Greiner — Subelliptic geometry [ MR 1486587 ]

Heinrich Begehr and Gerald N. Hile — Higher order Cauchy Pompeiu operators [ MR 1486588 ]

Mischa Cotlar and Cora Sadosky — A polydisk version of Beurling’s characterization for invariant subspaces of finite multicodimension [ MR 1486589 ]

Bert Fischer and Nikolai Tarkhanov — A representation of solutions with singularities [ MR 1486590 ]

Edwin Franks and John Ryan — Bounded monogenic functions on unbounded domains [ MR 1486591 ]

M. Gromov, G. Henkin and M. Shubin — $L^2$ holomorphic functions on pseudoconvex coverings [ MR 1486592 ]

Klaus Gürlebeck — On some operators in Clifford analysis [ MR 1486593 ]

U. Hagenbach and H. Upmeier — Toeplitz $C^*$algebras over nonconvex cones and pseudosymmetric spaces [ MR 1486594 ]

A. M. Kytmanov and S. G. Myslivets — On an application of the BochnerMartinelli operator [ MR 1486595 ]

N. K. Karapetyants — Local estimates for fractional integral operators and potentials [ MR 1486596 ]

Chun Li and Zhijian Wu — Hankel operators on Clifford valued Bergman space [ MR 1486597 ]

Mircea Martin and Norberto Salinas — Weitzenböck type formulas and joint seminormality [ MR 1486598 ]

V. S. Rabinovich — $C^*$algebras of pseudodifferential operators and limit operators [ MR 1486599 ]

Enrique Ramírez de Arellano and Nikolai Vasilevski — Bargmann projection, threevalued functions and corresponding Toeplitz operators [ MR 1486600 ]

R. Michael Range — Singular integral operators in the $\overline \partial $ theory on convex domains in ${\bf C}^n$ [ MR 1486601 ]

Stefan G. Samko — Differentiation and integration of variable order and the spaces $L^{p(x)}$ [ MR 1486602 ]

A. G. Sergeev — Twistor quantization of loop spaces and general Kähler manifolds [ MR 1486603 ]

Michael Shapiro and Luis Manuel Tovar — On a class of integral representations related to the twodimensional Helmholtz operator [ MR 1486604 ]

M. M. Smirnov — Cocycles on the gauge group and the algebra of ChernSimons classes [ MR 1486605 ]

Wolfgang Sprössig — Boundary value problems treated with methods of Clifford analysis [ MR 1486606 ]

Franciszek Hugon Szafraniec — Analytic models of the quantum harmonic oscillator [ MR 1486607 ]

Alexander Turbiner — Interesting relations in Fock space [ MR 1486608 ]

André Unterberger — Quantization: some problems, tools, and applications [ MR 1486609 ]