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Complex analysis : (Record no. 13686)

MARC details
000 -LEADER
fixed length control field	02122nam a2200217 a 4500
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN	0387909931 (paperback)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN	9780387909936 (paperback)
100 1# - MAIN ENTRY--AUTHOR NAME
Personal name	Luecking, D.H.
245 10 - TITLE STATEMENT
Title	Complex analysis :
250 ## - EDITION STATEMENT
Edition statement	Softcover reprint of the original 1st ed. 1984.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication	[S.l.] :
Name of publisher	Springer,
Year of publication	1984.
300 ## - PHYSICAL DESCRIPTION
Number of Pages	176 p. ;
490 1# - SERIES STATEMENT
Series statement	Universitext.
520 ## - SUMMARY, ETC.
Summary, etc	The main idea of this book is to present a good portion of the standard material on functions of a complex variable, as well as some new material, from the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which concretely identifies the dual of H(G) with the space of germs of holomorphic functions on the complement of G. From this result, for example, Runge's approximation theorem and the global Cauchy integral theorem follow in a few short steps. Other consequences of this duality theorem are the Germay interpolation theorem and the Mittag-Leffler Theorem. The approach via duality is entirely consistent with Cauchy's approach to complex variables, since curvilinear integrals are typical examples of linear functionals. The prerequisite for the book is a one-semester course in com� plex variables at the undergraduate-graduate level, so that the elements of the local theory are supposed known. In particular, the Cauchy Theorem for the square and the circle are assumed, but not the global Cauchy Theorem in any of its forms. The second author has three times taught a graduate course based on this material at the University of Illinois, with good results.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name	Rubel, Lee A.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier	http://www.amazon.com/exec/obidos/ASIN/0387909931/chopaconline-20

Holdings
Withdrawn status	Lost status	Home library	Current library	Date acquired	Cost, normal purchase price	Full call number	Accession Number	Koha item type
		Seminar Library, Mathematics & Statis.	Seminar Library, Mathematics & Statis.	10/08/2015	1248.00	515.9LUE	10469	Books