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Subharmonic Functions
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Book Synopsis Subharmonic Functions, Generalizations, Holomorphic Functions, Meromorphic Functions, and Properties. by : Juhani Riihentaus
Download or read book Subharmonic Functions, Generalizations, Holomorphic Functions, Meromorphic Functions, and Properties. written by Juhani Riihentaus and published by Bentham Science Publishers. This book was released on 2021-05-20 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains different types of subharmonic and harmonic functions. The book brings 12 chapters explaining general and specific types of subharmonic functions (eg. quasinearly subharmonic functions and other separate functions), related partial differential equations, mathematical proofs and extension results. The methods covered in the book also attempt to explain different mathematical analyses such as elliptical equations, domination conditions, weighted boundary behavior. The book serves as a reference work for scholars interested in potential theory and complex analysis.
Book Synopsis On the Problem of Plateau / Subharmonic Functions by : T. Rado
Download or read book On the Problem of Plateau / Subharmonic Functions written by T. Rado and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: A convex function f may be called sublinear in the following sense; if a linear function l is ::=: j at the boundary points of an interval, then l:> j in the interior of that interval also. If we replace the terms interval and linear junction by the terms domain and harmonic function, we obtain a statement which expresses the characteristic property of subharmonic functions of two or more variables. This ge neralization, formulated and developed by F. RIEsz, immediately at tracted the attention of many mathematicians, both on account of its intrinsic interest and on account of the wide range of its applications. If f (z) is an analytic function of the complex variable z = x + i y. then If (z) I is subharmonic. The potential of a negative mass-distribu tion is subharmonic. In differential geometry, surfaces of negative curvature and minimal surfaces can be characterized in terms of sub harmonic functions. The idea of a subharmonic function leads to significant applications and interpretations in the fields just referred to, and· conversely, every one of these fields is an apparently in exhaustible source of new theorems on subharmonic functions, either by analogy or by direct implication.
Book Synopsis Growth Theory of Subharmonic Functions by : Vladimir S. Azarin
Download or read book Growth Theory of Subharmonic Functions written by Vladimir S. Azarin and published by Springer Science & Business Media. This book was released on 2008-10-20 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables. The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function. All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions.
Book Synopsis Subharmonic Functions by : W. K. Hayman
Download or read book Subharmonic Functions written by W. K. Hayman and published by Elsevier. This book was released on 2014-06-28 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable. The material also has applications in differential equations and differential equations and differential geometry. It reflects the increasingly important role that subharmonic functions play in these areas of mathematics. The presentation goes back to the pioneering work of Ahlfors, Heins, and Kjellberg, leading to and including the more recent results of Baernstein, Weitsman, and many others. The volume also includes some previously unpublished material. It addresses mathematicians from graduate students to researchers in the field and will also appeal to physicists and electrical engineers who use these tools in their research work. The extensive preface and introductions to each chapter give readers an overview. A series of examples helps readers test their understatnding of the theory and the master the applications.
Book Synopsis Entire and Subharmonic Functions by :
Download or read book Entire and Subharmonic Functions written by and published by American Mathematical Soc.. This book was released on 1992 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complex Analysis by : Theodore W. Gamelin
Download or read book Complex Analysis written by Theodore W. Gamelin and published by Springer Science & Business Media. This book was released on 2013-11-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.
Book Synopsis Introduction to Holomorphic Functions of Several Variables by : R.C. Gunning
Download or read book Introduction to Holomorphic Functions of Several Variables written by R.C. Gunning and published by CRC Press. This book was released on 1990-05-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently.
Book Synopsis Function Theory of One Complex Variable by : Robert Everist Greene
Download or read book Function Theory of One Complex Variable written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 2006 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.
Book Synopsis Harmonic and Subharmonic Function Theory on the Hyperbolic Ball by : Manfred Stoll
Download or read book Harmonic and Subharmonic Function Theory on the Hyperbolic Ball written by Manfred Stoll and published by Cambridge University Press. This book was released on 2016-06-30 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is made accessible to a broad audience as it does not require any knowledge of Lie groups and only a limited knowledge of differential geometry. The author's primary emphasis is on potential theory on the hyperbolic ball, but many other relevant results for the hyperbolic upper half-space are included both in the text and in the end-of-chapter exercises. These exercises expand on the topics covered in the chapter and involve routine computations and inequalities not included in the text. The book also includes some open problems, which may be a source for potential research projects.
Book Synopsis Holomorphic Functions of Several Variables by : Ludger Kaup
Download or read book Holomorphic Functions of Several Variables written by Ludger Kaup and published by Walter de Gruyter. This book was released on 1983 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Book Synopsis Subharmonic Functions by : Tibor Radó
Download or read book Subharmonic Functions written by Tibor Radó and published by Springer-Verlag. This book was released on 2013-12-11 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Book Synopsis Introduction to the Theory of Entire Functions of Several Variables by : Lev Isaakovich Ronkin
Download or read book Introduction to the Theory of Entire Functions of Several Variables written by Lev Isaakovich Ronkin and published by American Mathematical Soc.. This book was released on 1974 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Complex Variables by : Steven G. Krantz
Download or read book Handbook of Complex Variables written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading the text is minimal: a good ground ing in (real variable) calculus will suffice. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. This book is a handy com pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.
Book Synopsis Holomorphic Functions and Integral Representations in Several Complex Variables by : R. Michael Range
Download or read book Holomorphic Functions and Integral Representations in Several Complex Variables written by R. Michael Range and published by Springer Science & Business Media. This book was released on 1998-06-26 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Function Classes on the Unit Disc by : Miroslav Pavlović
Download or read book Function Classes on the Unit Disc written by Miroslav Pavlović and published by Walter de Gruyter. This book was released on 2013-12-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains a study on various function classes, a number of new results and new or easy proofs of old results (Fefferman-Stein theorem on subharmonic behavior, theorems on conjugate functions and fractional integration on Bergman spaces, Fefferman's duality theorem), which are interesting for specialists; applications of the Hardy-Littlewood inequalities on Taylor coefficients to (C, α)-maximal theorems and (C, α)-convergence; a study of BMOA, due to Knese, based only on Green's formula; the problem of membership of singular inner functions in Besov and Hardy-Sobolev spaces; a full discussion of g-function (all p > 0) and Calderón's area theorem; a new proof, due to Astala and Koskela, of the Littlewood-Paley inequality for univalent functions; and new results and proofs on Lipschitz spaces, coefficient multipliers and duality, including compact multipliers and multipliers on spaces with non-normal weights. It also contains a discussion of analytic functions and lacunary series with values in quasi-Banach spaces with applications to function spaces and composition operators. Sixteen open questions are posed. The reader is assumed to have a good foundation in Lebesgue integration, complex analysis, functional analysis, and Fourier series. Further information can be found at the author's website at http://poincare.matf.bg.ac.rs/~pavlovic.
Book Synopsis Analytic Functions by : M.A. Evgrafov
Download or read book Analytic Functions written by M.A. Evgrafov and published by Courier Dover Publications. This book was released on 2019-09-18 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly regarded text is directed toward advanced undergraduates and graduate students in mathematics who are interested in developing a firm foundation in the theory of functions of a complex variable. The treatment departs from traditional presentations in its early development of a rigorous discussion of the theory of multiple-valued analytic functions on the basis of analytic continuation. Thus it offers an early introduction of Riemann surfaces, conformal mapping, and the applications of residue theory. M. A. Evgrafov focuses on aspects of the theory that relate to modern research and assumes an acquaintance with the basics of mathematical analysis derived from a year of advanced calculus. Starting with an introductory chapter containing the fundamental results concerning limits, continuity, and integrals, the book addresses analytic functions and their properties, multiple-valued analytic functions, singular points and expansion in series, the Laplace transform, harmonic and subharmonic functions, extremal problems and distribution of values, and other subjects. Chapters are largely self-contained, making this volume equally suitable for the classroom or independent study.
Download or read book Bounded Analytic Functions written by and published by Academic Press. This book was released on 1981-10-12 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bounded Analytic Functions
