Theory of Complex Functions, R.B. Burckel; Reinhold Remmert
Автор: HENKIN; LEITERER Название: Theory of Functions on Complex Manifolds ISBN: 3034865392 ISBN-13(EAN): 9783034865395 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Conway Название: Functions of One Complex Variable I ISBN: 0387903283 ISBN-13(EAN): 9780387903286 Издательство: Springer Рейтинг: Цена: 6981.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: "This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year`s course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis.
Описание: Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.Key Features: - The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings- Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra- Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal- Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula- The method of diophantine approximation is used to study self-similar strings and flows- Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functionsThroughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts.The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.
Автор: John B. Conway Название: Functions of One Complex Variable II ISBN: 0387944605 ISBN-13(EAN): 9780387944609 Издательство: Springer Рейтинг: Цена: 6841.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Addresses many problems on the theory of functions of one complex variable. This book treats several topics in geometric function theory and potential theory in the plane, such as conformal equivalence for simply connected regions, de Branges` proof of the Bieberbach conjecture, Hardy spaces on the disk, and potential theory in the plane.
Описание: This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial different
Автор: Pierre Lelong; Lawrence Gruman Название: Entire Functions of Several Complex Variables ISBN: 3642703461 ISBN-13(EAN): 9783642703461 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Автор: John B. Conway Название: Functions of One Complex Variable II ISBN: 1461269113 ISBN-13(EAN): 9781461269113 Издательство: Springer Рейтинг: Цена: 5589.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the sequel to my book Functions of One Complex Variable I, and probably a good opportunity to express my appreciation to the mathemat- ical community for its reception of that work. In retrospect, writing that book was a crazy venture. As a graduate student I had had one of the worst learning experiences of my career when I took complex analysis; a truly bad teacher. As a non-tenured assistant professor, the department allowed me to teach the graduate course in complex analysis. They thought I knew the material; I wanted to learn it. I adopted a standard text and shortly after beginning to prepare my lectures I became dissatisfied. All the books in print had virtues; but I was educated as a modern analyst, not a classical one, and they failed to satisfy me. This set a pattern for me in learning new mathematics after I had become a mathematician. Some topics I found satisfactorily treated in some sources; some I read in many books and then recast in my own style. There is also the matter of philosophy and point of view. Going from a certain mathematical vantage point to another is thought by many as being independent of the path; certainly true if your only objective is getting there. But getting there is often half the fun and often there is twice the value in the journey if the path is properly chosen.
Автор: John B. Conway Название: Functions of One Complex Variable I ISBN: 0387942343 ISBN-13(EAN): 9780387942346 Издательство: Springer Рейтинг: Цена: 6981.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: "This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year`s course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis.
Описание: 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.
Автор: G. Jameson Название: A First Course on Complex Functions ISBN: 0412097109 ISBN-13(EAN): 9780412097102 Издательство: Springer Рейтинг: Цена: 12157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book contains a rigorous coverage of those topics (and only those topics) that, in the author`s judgement, are suitable for inclusion in a first course on Complex Functions.
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