Download or read book Growth Properties of Complex Valued Functions written by Sanjib Kumar Datta and published by LAP Lambert Academic Publishing. This book was released on 2015-02-16 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1926 Finnish mathematician Rolf Nevanlinna initiated the value distrib- ution theory of complex valued functions. Actually this theory deals with the study of the fact how an entire or meromorphic function assumes some values and the inuence of assuming certain values in some specic manner on a func- tion. In fact, the well known fundamental theorem of classical algebra is prob- ably the rst value distribution theorem. The value distribution theory deals with the various aspects of the behavior of entire and meromorphic functions one of which is the study of comparative growth properties. The present book deals with the measure of growth rates of composite entire and meromorphic functions on the basis of integer translation, estimation of generalized growth properties via maximum terms of composite entire functions as well as those of di erential monomials, wronskians, di erential polynomials etc. generated by them and growth analysis of iterated entire functions with a treatment of their maximum terms.
Download or read book On the Growth Properties of a Function of Two Complex Variables Given by Its Power Series Expansion written by Abe Gelbart and published by . This book was released on 1940 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Growth Properties of Vector valued Analytic Functions written by Daniel O'Connell Etter and published by . This book was released on 1962 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Generalized Growth rates of Integer Translated Entire and Meromorphic Functions written by Tanmay Biswas and published by Bentham Science Publishers. This book was released on 2023-03-28 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of entire and meromorphic functions is a very important area of complex analysis. This monograph aims to expand the discussion about some growth properties of integer translated composite entire and meromorphic functions on the basis of their (p,q,t)L order and (p,q,t)L type. This book presents six chapters. Chapter 1 introduces the reader to the preliminary definitions and notations. Chapter 2 and Chapter 3 discuss some results related to (p; q; t) Lth order and (p; q; t)Lth lower order of composite entire and meromorphic functions on the basis of their integer translation. Chapter 4 establishes some relations of integer translated composite entire and meromorphic functions based on their (p; q; t) Lth type and (p; q; t) Lth weak type. Chapter 5 deals with some results about (p; q; t) Lth order and (p; q; t) Lth type of composite entire and meromorphic functions on the basis of their integer translation. Chapter 6 focuses on some results about (p; q; t) Lth order and (p; q; t) Lth type of composite entire and meromorphic functions on the basis of their integer translation. This monograph will be very helpful for postgraduates, researchers, and faculty members interested in value distribution theorems in complex mathematical analysis.
Download or read book Complex valued Functions with Real Domains written by Ray Frank Gilbert and published by . This book was released on 1965 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Entire Functions of Several Complex Variables written by Pierre Lelong and published by Springer. This book was released on 1986-03 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. 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. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.
Download or read book Functions of a Complex Variable written by E. J. Townsend and published by Forgotten Books. This book was released on 2015-06-17 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Functions of a Complex Variable The present volume is based on a course of lectures given by the author for a number of years at the University of Illinois. It is intended as an introductory course suitable for first year graduate students and assumes a knowledge of only such fundamental principles of analysis as the student will have had upon completing the usual first course in calculus. Such additional information concerning functions of real variables as is needed in the development of the subject has been introduced as a regular part of the text. Thus a discussion of the general properties of line-integrals, a proof of Green's theorem, etc., have been included. The material chosen deals for the most part with the general properties of functions of a complex variable, and but little is said concerning the properties of some of the more special classes of functions, as for example elliptic functions, etc., since in a first course these subjects can hardly be treated in a satisfactory manner. The course presupposes no previous knowledge of complex numbers and the order of development is much as that commonly followed in the calculus of real variables. Integration is introduced early, in connection with differentiation. In fact the first statement of the necessary and sufficient condition that a function is holomorphic in a given region is made in terms of an integral. By this order of arrangement, it is possible to establish early in the course the fact that the continuity of the derivative follows from its existence, and consequently the Cauchy-Goursat and allied theorems can be demonstrated without any assumption as to such continuity. Likewise, it can thus be shown that Laplace's differential equation is satisfied without making the usual assumptions as to the existence of the derivatives of second order. The term holomorphic, often omitted, has been used as expressing an important property of single-valued functions, reserving the use of the term analytic for use in connection with functions derived from a given element by means of analytic continuation. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Complex Numbers in n Dimensions written by S. Olariu and published by Elsevier. This book was released on 2002-06-20 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined. The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers. The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functions of the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions. In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible. The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.
Download or read book Growth Properties of Entire Functions Depending on a Parameter written by Stefan Halvarsson and published by . This book was released on 1994 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Real and Complex Analysis written by Christopher Apelian and published by CRC Press. This book was released on 2009-12-08 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents Real & Complex Analysis Together Using a Unified Approach A two-semester course in analysis at the advanced undergraduate or first-year graduate level Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide. By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website. This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.
Download or read book Complex Analysis written by Jerry R. Muir, Jr. and published by John Wiley & Sons. This book was released on 2015-05-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.
Download or read book Growth properties of analytic and plurisubharmonic functions of finite order written by Ragnar Sigurdsson and published by . This book was released on 1984 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Analysis and Special Topics in Harmonic Analysis written by Carlos A. Berenstein and published by Springer. This book was released on 1995-08-04 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schwartz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic analysis. By providing an overview of current research and open problems, as well as topics that have wide applications in engineering, this book should be of interest to mathematicians and applied mathematicians, as well as to graduate students beginning their research.
Download or read book Growth Properties of Solutions of Schr dinger Type Systems written by Gholamreza Baradaran Khosrovshahi and published by . This book was released on 1972 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Analysis written by V. Karunakaran and published by Alpha Science International Limited. This book was released on 2002 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work introduces Complex Analysis to undergraduate and postgraduate students. The only prerequisites are rudiments of real analysis and linear algebra. Special features include: an integrated approach to the concept of differentiation for Complex valued functions of a Complex variable; unified Cauchy Riemann equations; a detailed discussion on the construction of Riemann Surfaces for elementary functions leading to its abstract concept; step by step development of the most general form of Cauchy theorem; complex version of real intermediate value theorem; exhaustive treatment of contour integration; and an introduction to the theory of univalent functions on the unit disc including a brief history of the Bieberbach's conjecture and its solutions.
Download or read book Complex Valued Modeling in Economics and Finance written by Sergey Svetunkov and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex-Valued Modeling in Economics and Finance outlines the theory, methodology, and techniques behind modeling economic processes using complex variables theory. The theory of complex variables functions is widely used in many scientific fields, since work with complex variables can appropriately describe different complex real-life processes. Many economic indicators and factors reflecting the properties of the same object can be represented in the form of complex variables. By describing the relationship between various indicators using the functions of these variables, new economic and financial models can be created which are often more accurate than the models of real variables. This book pays critical attention to complex variables production in stock market modeling, modeling illegal economy, time series forecasting, complex auto-aggressive models, and economic dynamics modeling. Very little has been published on this topic and its applications within the fields of economics and finance, and this volume appeals to graduate-level students studying economics, academic researchers in economics and finance, and economists.
Download or read book Entire Functions of Several Complex Variables written by Pierre Lelong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. 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. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.
