Overview
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.
Full Product Details
Author: Reynaldo Rocha-Chavez ,
Michael Shapiro ,
Frank Sommen ,
Haim Brezis
Publisher: Taylor & Francis Inc
Imprint: Chapman & Hall/CRC
Dimensions:
Width: 15.60cm
, Height: 1.30cm
, Length: 23.40cm
Weight: 0.380kg
ISBN: 9781584882466
ISBN 10: 1584882468
Pages: 214
Publication Date: 03 August 2001
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: In Print
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Reviews
the book will be interesting to specialists in complex analysis and its applications. - Mathematical Reviews, 2003a This well-written book is a valuable contribution to the broad field of interactions between complex analysis and partial differential equations...Moreover, the book can be used for individual studies, because fundamental concepts and important theorems are explained in detail. -Mathematical Reviews, Issue 94a
Author Information
Reynaldo Rocha-Chavez, Michael Shapiro, Frank Sommen
