Integral Theorems for Functions and Differential Forms in C(m)
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A01=Frank Sommen
A01=Michael Shapiro
A01=Reynaldo Rocha-Chavez
advanced mathematical analysis
algebra
analysis
Antiholomorphic Functions
Author_Frank Sommen
Author_Michael Shapiro
Author_Reynaldo Rocha-Chavez
Bounded Domain
Category=PBKF
Category=PBKJ
Cauchy Integral Theorem
Cauchy Kernel
Cauchy Riemann Equation
Class C1
Class C2
clifford
Clifford Algebra
Clifford analysis
complex
Complex Algebra
complex Hodge-Dolbeault
Differential Form
differential forms applications
Dirac Operator
Dirac operators
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
equalities
Equalities Hold
gE
grassmann
hold
Holds
Holomorphic Function
Integral Representation
Integral Theorem
laplace
linear
Morera Theorem
operators
Piecewise Smooth Boundary
Piecewise Smooth Surface
Quaternionic Analysis
reproducing kernel theory
several complex variables
Smooth
Stokes Formula
Topological Boundary
Product details
- ISBN 9781584882466
- Weight: 380g
- Dimensions: 156 x 234mm
- Publication Date: 03 Aug 2001
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Paperback
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The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more and more paradoxical differences between the structures of the two theories.
The authors of this Research Note were driven by the quest to construct a theory in several complex variables that has the same structure as the one-variable theory. That is, they sought a reproducing kernel for the whole class that is universal and from same class. Integral Theorems for Functions and Differential Forms in Cm documents their success. Their highly original approach allowed them to obtain new results and refine some well-known results from the classical theory of several complex variables. The 'hyperholomorphic" theory they developed proved to be a kind of direct sum of function theories for two Dirac-type operators of Clifford analysis considered in the same domain.
In addition to new results and methods, this work presents a first-look at a brand new setting, based upon the natural language of differential forms, for complex analysis. Integral Theorems for Functions and Differential Forms in Cm reveals a deep link between the fields of several complex variables theory and Clifford analysis. It will have a strong influence on researchers in both areas, and undoubtedly will change the general viewpoint on the methods and ideas of several complex variables theory.
Reynaldo Rocha-Chavez, Michael Shapiro, Frank Sommen
