國立臺灣大學數學系圖書室-An Introduction to Complex Analysis in Several Variables

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An Introduction to Complex Analysis in Several Variables

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Rolf H. Nevanlinna Introduction to complex analysis
- Nevanlinna 是 Ahlfors 的老師，他寫書非常清楚，不會把簡單的東西寫得很難。初學者應該唸這本書。在內容方面，他有提到一些 Riemann surfaces ，而 prime number theory 及 zeta functions 也算是本書的特色之一。[陳金次、張海潮老師]
- {The second edition has been reviewed [1973; MR0344507].}
  From the preface to the third edition: ``Quite a few monographs on various aspects of complex analysis in several variables have appeared since the first edition of this book was published, but none of them uses the analytic techniques based on the solution of the ∂¯¯¯ Neumann problem as the main tool. The additions made in this edition have therefore been chosen so that they place additional stress on results where these methods are particularly important. Thus we have added a section 7.7 which presents Ehrenpreis' `fundamental principle' in full. This has also required a number of modifications of the earlier section 7.6 on `cohomology with bounds'. The local arguments in section 7.7 are closely related to the proof of the coherence of the sheaf of germs of functions vanishing on an analytic set. For this reason it has been included in a new section 6.5, which eliminates a conspicuous omission in the earlier editions. Finally, we have added a discussion of the theorem of Siu on the Lelong numbers of plurisubharmonic functions since the L2 techniques are essential in the proof and plurisubharmonic functions play such an important role in this book that it seems natural to discuss their main singularities.'' [form MathSciNet]