Book Details
Search page | 
Title Index
| Author Index
Marek Jarnicki (Jagiellonian University, Kraków, Poland)
Peter Pflug (University of Oldenburg, Germany)
Separately Analytic Functions
ISBN print 978-3-03719-098-2, ISBN online 978-3-03719-598-7DOI 10.4171/098
August 2011, 306 pages, hardcover, 17 x 24 cm.
58.00 Euro
The story of separately holomorphic functions began about 100 years ago.
During the second half of the 19th century, it became known that a separately
continuous function is not necessarily continuous as a function of all
variables. At the beginning of the 20th century, the study of separately
holomorphic functions started due to the fundamental work of Osgood and
Hartogs. This book provides the first self-contained and complete presentation of the
study of separately holomorphic functions, starting from its birth up to
current research. Most of the results presented have never been published
before in book form. The text is divided into two parts. A more elementary
one deals with separately holomorphic functions “without singularities”,
another addresses the situation of existing singularities. A discussion of the
classical results related to separately holomorphic functions leads to the
most fundamental result, the classical cross theorem as well as various
extensions and generalizations to more complicated “crosses”. Additionally,
several applications for other classes of “separately regular” functions are
given. A solid background in basic complex analysis is a prerequisite. In order to
make the book self-contained, all the results needed for its understanding
are collected in special introductory chapters and referred to at the beginning
of each section. The book is addressed to students and researchers in several complex
variables as well as to mathematicians and theoretical physicists who are
interested in this area of mathematics.
Keywords: Separately holomorphic/meromorphic functions, Riemann domains, N-fold crosses, generalized crosses, relative extremal functions, holomorphic extension with singularities
BACK TO TOP