Several Complex Variables Iii

Author: G.M. Khenkin
Publisher: Springer Science & Business Media
ISBN: 364261308X
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We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space

Several Complex Variables Iv

Author: Semen Gindikin
Publisher: Springer Science & Business Media
ISBN: 3642612636
Size: 71.55 MB
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This volume of the EMS contains four survey articles on analytic spaces. They are excellent introductions to each respective area. Starting from basic principles in several complex variables each article stretches out to current trends in research. Graduate students and researchers will find a useful addition in the extensive bibliography at the end of each article.

Several Complex Variables Ii

Author: G.M. Khenkin
Publisher: Springer Science & Business Media
ISBN: 3642578829
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Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given.

Algebraic Geometry Ii

Author: I.R. Shafarevich
Publisher: Springer Science & Business Media
ISBN: 3642609252
Size: 68.14 MB
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This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

Several Complex Variables Vii

Author: H. Grauert
Publisher: Springer Science & Business Media
ISBN: 3662098733
Size: 12.62 MB
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The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field. The book contains an introduction written by Remmert, describing the history of the subject, and is very useful to graduate students and researchers in complex analysis, algebraic geometry and differential geometry.

Several Complex Variables Vi

Author: Reinhold Remmert
Publisher: Springer
ISBN: 9783540527886
Size: 68.37 MB
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The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme. Some of the topics dealt with are the following: recent developments in the theory of proper holomorphic maps; the enormous influence and power of Hodge structures (and families of such structures); the mutual influence of complex analysis and representation theory in the study of (almost) homogeneous complex manifolds; the influence of ideas from mathematical physics (via the Yang-Mills equation and stable vector bundles) on the study of the topology of complex algebraic surfaces; the fruitfulness of studying spaces of compact Riemann surfaces and of compact Kähler manifolds from the point of view of the curvature of theses spaces. Thus, the present volume should provide some idea of the richness of the theory of complex manifolds.

Number Theory Iii

Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 3642582273
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In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see [La 9Oc]. The field of diophantine geometry is now moving quite rapidly. Out standing conjectures ranging from decades back are being proved. I have tried to give the book some sort of coherence and permanence by em phasizing structural conjectures as much as results, so that one has a clear picture of the field. On the whole, I omit proofs, according to the boundary conditions of the encyclopedia. On some occasions I do give some ideas for the proofs when these are especially important. In any case, a lengthy bibliography refers to papers and books where proofs may be found. I have also followed Shafarevich's suggestion to give examples, and I have especially chosen these examples which show how some classical problems do or do not get solved by contemporary in sights. Fermat's last theorem occupies an intermediate position. Al though it is not proved, it is not an isolated problem any more.

Analysis Iii

Author: S. M. Nikol'skij
Publisher: Springer Verlag
ISBN: 9780387518664
Size: 41.66 MB
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Dynamical Systems

Author: D. V. Anosov
Publisher:
ISBN: 9783540533764
Size: 71.53 MB
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