Download or read book On Growth of Subharmonic Functions in Space written by Iman Abdulhafiz Itani and published by . This book was released on 2008 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let u be a subharmonic function in m-dimensional real space. The study of the gr owth of u from the point of view of classical value distribution theory is a sub ject of great interest. The idea is to compare the Lp means of u on a sphere of radius r with the Reisz mass of u in that same sphere. In the two dimensional ca se, numerous results are known. But they do not all carry over to higher dimensi ons. Certain difficulties arise in higher dimensions which do not occur in dimen sion 2. For example, a subharmonic function in the Euclidean space of dimension more than 4 may fail to be square integrable over a sphere. In this thesis we propose to study such growth problems outlining the similariti es and differences between the two dimensional case and the higher dimensional c ases. The study will involve: (i) a survey of the main functionals used in class ical value distribution theory and the corresponding inequalities satisfied by t hem. (ii) definitions of corresponding functionals in the setting of subharmonic functions in m dimensional real space and statements of main theorems governing them. (iii) Calculation of spherical harmonics for a special class of such func tions. (iv) Effect of one kind of symmetrization of the Reisz mass on the size o f spherical harmonics for two classes of subharmonic functions. (v) Statement an d proof of main growth results; in particular, the L2-result when m = 2, 3, 4.
Download or read book On Functions Subharmonic in a Half space written by Alfred Huber and published by . This book was released on 1955 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
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.
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 2008-12-14 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.
Download or read book Growth Properties of Subharmonic Functions written by Björn Dahlberg and published by . This book was released on 1971 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
Download or read book Distribution of Zeros of Entire Functions written by Boris I_Akovlevich Levin and published by American Mathematical Soc.. This book was released on 1964-12-31 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Functions of Completely Regular Growth written by L.I. Ronkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with functions of completely regular growth (FCRG), i.e., functions that have, in some sense, good asymptotic behaviour out of an exceptional set. The theory of entire functions of completely regular growth of on variable, developed in the late 1930s, soon found applications in both mathematics and physics. Later, the theory was extended to functions in the half-plane, subharmonic functions in space, and entire functions of several variables. This volume describes this theory and presents recent developments based on the concept of weak convergence. This enables a unified approach and provides a comparatively simple presentation of the classical Levin-Pfluger theory. Emphasis is put on those classes of functions which are particularly important for applications -- functions having a bounded spectrum and finite exponential sums. For research mathematicians and physicists whose work involves complex analysis and its applications. The book will also be useful to those working in some areas of radiophysics and optics.
Download or read book Complex Methods in Approximation Theory written by Francisco Marcellán and published by Universidad Almería. This book was released on 1997-01-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date account of research in Approximation Theory and Complex Analysis, areas which are the subject of recent exciting developments.The level of presentation should be suitable for anyone with a good knowledge of analysis, including scientists with a mathematical background. The volume contains both research papers and surveys, presented by specialists in the field. The areas discussed are: Orthogonal Polynomials (with respect to classical and Sobolev inner products), Approximation in Several Complex Variables, Korovkin-type Theorems, Potential Theory, Ratinal Approximation and Linear Ordinary Differential Equations.
Download or read book Zeros and Growth of Entire Functions of Several Variables the Complex Monge Amp re Operator and Some Related Topics written by Xing Yang and published by . This book was released on 1992 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Analyticity in Infinite Dimensional Spaces written by Michel Hervé and published by Walter de Gruyter. This book was released on 2011-06-01 with total page 217 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. 30 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.
Download or read book Theory of Hp Spaces written by Peter L. Duren and published by Courier Dover Publications. This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A blend of classical and modern techniques and viewpoints, this text examines harmonic and subharmonic functions, the basic structure of Hp functions, applications, Taylor coefficients, interpolation theory, more. 1970 edition.
Download or read book Integral Equations Boundary Value Problems And Related Problems written by Xing Li and published by World Scientific. This book was released on 2013-03-07 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.
Download or read book Complex Analysis And Potential Theory Proceedings Of The Conference Satellite To Icm 2006 written by T Aliyev Azeroglu and published by World Scientific. This book was released on 2007-08-13 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the contributions from outstanding mathematicians, such as Samuel Krushkal, Reiner Kühnau, Chung Chun Yang, Vladimir Miklyukov and others.It will help researchers to solve problems on complex analysis and potential theory and discuss various applications in engineering. The contributions also update the reader on recent developments in the field. Moreover, a special part of the volume is completely devoted to the formulation of some important open problems and interesting conjectures.
