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Titlebook: Introduction to Complex Analysis in Several Variables; Volker Scheidemann Book 20051st edition Birkhäuser Basel 2005 Biholomorphic maps.Ca

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发表于 2025-3-21 16:21:02 | 显示全部楼层 |阅读模式
书目名称Introduction to Complex Analysis in Several Variables
编辑Volker Scheidemann
视频video
概述Focused on students.Requires minimum of prerequisites.More than 50 examples, over 100 exercises.Includes supplementary material:
图书封面Titlebook: Introduction to Complex Analysis in Several Variables;  Volker Scheidemann Book 20051st edition Birkhäuser Basel 2005 Biholomorphic maps.Ca
描述The idea for this book came when I was an assistant at the Department of Mat- matics and Computer Science at the Philipps-University Marburg, Germany. S- eraltimesIfacedthetaskofsupportinglecturesandseminarsoncomplexanalysis of several variables and found out that there are very few books on the subject, compared to the vast amount of literature on function theory of one variable, let alone on real variables or basic algebra. Even fewer books, to my understanding, were written primarily with the student in mind. So it was quite hard to ?nd s- porting examples and exercises that helped the student to become familiar with the fascinating theory of several complex variables. Of course, there are notable exceptions, like the books of R.M. Range [9] or B. and L. Kaup [6], however, even those excellent books have a drawback: they are quite thick and thus quite expensive for a student’s budget. So an additional motivation to write this book was to give a comprehensive introduction to the theory of several complex variables, illustrate it with as many examples as I could ?nd and help the student to get deeper insight by giving lots of exercises, reaching from almost trivial to rather chall
出版日期Book 20051st edition
关键词Biholomorphic maps; Cartan-Thullen theory; Complex analysis; Complex variables; Holomorphic functions; Ku
版次1
doihttps://doi.org/10.1007/3-7643-7491-8
isbn_ebook978-3-7643-7491-4
copyrightBirkhäuser Basel 2005
The information of publication is updating

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发表于 2025-3-21 22:43:05 | 显示全部楼层
r this book came when I was an assistant at the Department of Mat- matics and Computer Science at the Philipps-University Marburg, Germany. S- eraltimesIfacedthetaskofsupportinglecturesandseminarsoncomplexanalysis of several variables and found out that there are very few books on the subject, compa
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Continuation on Tubular Domains,due to Bochner, which states that every function holomorphic on a tubular domain . can be holomorphically extended to the convex hull of .. Bochner’s Theorem, unlike Hartogs’ Kugelsatz, holds also in dimension 1. However, if . = 1 the theorem is trivial, because every tube domain in ℂ coincides with its convex hull.
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Cartan-Thullen Theory,n of holomorphy should be the maximal domain of existence of some holomorphic function. In this chapter we will work on the task to characterize those domains . ⊂ ℂ., on which no simultaneous extension phenomena occur.
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Analytic Sets, systems of equations. We will introduce the notion of codimension of an analytic set and show that in most cases analytic sets are “thin enough” that holomorphic functions defined outside an analytic set can be extended across the analytic set.
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