LEADER 02876nam 22003975a 450 001 9910151928903321 005 20110815234510.0 010 $a3-03719-598-3 024 70$a10.4171/098 035 $a(CKB)3710000000953869 035 $a(CH-001817-3)131-110815 035 $a(PPN)178155950 035 $a(EXLCZ)993710000000953869 100 $a20110815j20110811 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSeparately Analytic Functions$b[electronic resource] /$fMarek Jarnicki, Peter Pflug 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2011 215 $a1 online resource (306 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v16 330 $aThe 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. 606 $aCalculus & mathematical analysis$2bicssc 606 $aSeveral complex variables and analytic spaces$2msc 615 07$aCalculus & mathematical analysis 615 07$aSeveral complex variables and analytic spaces 686 $a32-xx$2msc 700 $aJarnicki$b Marek$0726136 702 $aPflug$b Peter 801 0$bch0018173 906 $aBOOK 912 $a9910151928903321 996 $aSeparately Analytic Functions$92566852 997 $aUNINA