Lectures on Several Complex Variables, Paul M. Gauthier
Àâòîð: Paul M. Gauthier Íàçâàíèå: Lectures on Several Complex Variables ISBN: 3319115103 ISBN-13(EAN): 9783319115108 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 11179.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: This monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functions, the Dirichlet problem, and meromorphic functions. Based on a course given at Universit de Montr al, this brief introduction covers areas of contemporary importance that are not mentioned in most treatments of the subject, such as modular forms, which are essential for Wiles' theorem and the unification of quantum theory and general relativity. Also covered is the Riemann manifold of a function, which generalizes the Riemann surface of a function of a single complex variable and is a topic that is well-known in one complex variable, but rarely treated in several variables. Many details, which are intentionally left out, as well as many theorems are stated as problems, providing students with carefully structured instructive exercises.
Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level. Lectures on Several Complex Variables will be of interest to advanced undergraduate and beginning undergraduate students, as well as mathematical researchers and professors.
Àâòîð: Pei-Chu Hu; Chung-Chun Yang Íàçâàíèå: Differentiable and Complex Dynamics of Several Variables ISBN: 079235771X ISBN-13(EAN): 9780792357711 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 15372.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: Presents a comprehensive survey on dynamics and related topics, such as Fatou-Julia type theory, the Ergodic theorem and invariant sets, hyperbolicity in differentiable or complex dynamics, iterant ion theory on Pm, complex dynamics in Cm and the foundations of differentiable and complex dynamics.
Àâòîð: J?rgen Leiterer; Semen G. Gindikin; Dmitrij N. Akh Íàçâàíèå: Several Complex Variables IV ISBN: 3642647669 ISBN-13(EAN): 9783642647666 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 14673.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: This volume of the EMS contains four survey articles on analytic spaces. 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.
Îïèñàíèå: The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu- lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ- ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com- plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
Îïèñàíèå: 4 Hardy-Toeplitz Operators Over Tubular Domains 267 4.
Àâòîð: G.M. Khenkin; Jaak Peetre; I.M. Dektyarev; O.M. Kh Íàçâàíèå: Several Complex Variables III ISBN: 3642647855 ISBN-13(EAN): 9783642647857 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 14673.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. 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.
Àâòîð: H. Grauert; F. Campana; Thomas Peternell; G. Dethl Íàçâàíèå: Several Complex Variables VII ISBN: 3642081509 ISBN-13(EAN): 9783642081507 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 23058.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: 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.
Îïèñàíèå: This volume provides a detailed description of important geometric settings encountered in multi-variable complex analysis. There is a thorough exposition of the harmonic analysis background, and treatment of topics of current interest.
Àâòîð: Alan Howard; Pit-Mann Wong Íàçâàíèå: Contributions to Several Complex Variables ISBN: 3528089644 ISBN-13(EAN): 9783528089641 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 12157.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: In 1960 Wilhelm Stoll joined the University of Notre Dame faculty as Professor of Mathematics, and in October, 1984 the university acknowledged his many years of distinguished service by holding a conference in complex analysis in his honour.
Àâòîð: Takeo Ohsawa Íàçâàíèå: L? Approaches in Several Complex Variables ISBN: 4431562966 ISBN-13(EAN): 9784431562962 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 9781.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå:
Part I Holomorphic Functions and Complex Spaces.- Convexity Notions.- Complex Manifolds.- Classical Questions of Several Complex Variables.- Part II The Method of L Estimates.- Basics of Hilb
ert Space Theory.- Harmonic Forms.- Vanishing Theorems.- Finiteness Theorems.- Notes on Complete Kahler Domains (= CKDs).- Part III L Variant of Oka-Cartan Theory.- Extension Theorems.- Division Theorems.- Multiplier Ideals.- Part IV Bergman Kernels.- The Bergman Kernel and Metric.- Bergman Spaces and Associated Kernels.- Sequences of Bergman Kernels.- Parameter Dependence.- Part V L Approaches to Holomorphic Foliations.- Holomorphic Foliation and Stable Sets.- L Method Applied to Levi Flat Hypersurfaces.- LFHs in Tori and Hopf Surfaces.
Îïèñàíèå: This book reviews higher dimensional Nevanlinna theory and its relationship with Diophantine approximation theory. Coverage builds up from the classical theory of meromorphic functions on the complex plane with full proofs, to the current state of research.
Àâòîð: Pierre Lelong; Lawrence Gruman Íàçâàíèå: Entire Functions of Several Complex Variables ISBN: 3642703461 ISBN-13(EAN): 9783642703461 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 12577.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp- totic growth or optimal solutions in some sense.
