Asymptotic Behavior Of Generalized Functions PDF Download

Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Asymptotic Behavior Of Generalized Functions PDF full book. Access full book title Asymptotic Behavior Of Generalized Functions.

Asymptotic Behavior of Generalized Functions

Asymptotic Behavior of Generalized Functions
Author: Stevan Pilipovic
Publisher: World Scientific
Total Pages: 309
Release: 2012
Genre: Mathematics
ISBN: 9814366854
GET BOOK

Download Asymptotic Behavior of Generalized Functions Book in PDF, ePub and Kindle

The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach OCo of Estrada, Kanwal and Vindas OCo is related to moment asymptotic expansions of generalized functions and the Ces''aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.

Generalized Functions and Their Applications

Generalized Functions and Their Applications
Author: R.S. Pathak
Publisher: Springer Science & Business Media
Total Pages: 298
Release: 2013-11-11
Genre: Social Science
ISBN: 1489915915
GET BOOK

Download Generalized Functions and Their Applications Book in PDF, ePub and Kindle

The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.

Asymptotic Analysis

Asymptotic Analysis
Author: Ricardo Estrada
Publisher: Springer Science & Business Media
Total Pages: 266
Release: 2012-12-06
Genre: Mathematics
ISBN: 1468400290
GET BOOK

Download Asymptotic Analysis Book in PDF, ePub and Kindle

Asymptotic analysis is an old subject that has found applications in vari ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also pro vide a systematic procedure to assign values to the divergent integrals that often appear in the literature.

A Distributional Approach to Asymptotics

A Distributional Approach to Asymptotics
Author: Ricardo Estrada
Publisher: Springer Science & Business Media
Total Pages: 467
Release: 2012-09-08
Genre: Mathematics
ISBN: 0817681302
GET BOOK

Download A Distributional Approach to Asymptotics Book in PDF, ePub and Kindle

"...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic

Frontiers In Orthogonal Polynomials And Q-series

Frontiers In Orthogonal Polynomials And Q-series
Author: M Zuhair Nashed
Publisher: World Scientific
Total Pages: 577
Release: 2018-01-12
Genre: Mathematics
ISBN: 981322889X
GET BOOK

Download Frontiers In Orthogonal Polynomials And Q-series Book in PDF, ePub and Kindle

This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.

Introduction to Asymptotics and Special Functions

Introduction to Asymptotics and Special Functions
Author: F. W. J. Olver
Publisher: Academic Press
Total Pages: 312
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483267083
GET BOOK

Download Introduction to Asymptotics and Special Functions Book in PDF, ePub and Kindle

Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.

Pseudo-Regularly Varying Functions and Generalized Renewal Processes

Pseudo-Regularly Varying Functions and Generalized Renewal Processes
Author: Valeriĭ V. Buldygin
Publisher: Springer
Total Pages: 482
Release: 2018-10-12
Genre: Mathematics
ISBN: 3319995375
GET BOOK

Download Pseudo-Regularly Varying Functions and Generalized Renewal Processes Book in PDF, ePub and Kindle

One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors’ research work and approach – first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory.

On the Asymptotic Generalized Order Statistics and Related Functions

On the Asymptotic Generalized Order Statistics and Related Functions
Author: Haroon Barakat
Publisher: LAP Lambert Academic Publishing
Total Pages: 120
Release: 2012
Genre:
ISBN: 9783659303449
GET BOOK

Download On the Asymptotic Generalized Order Statistics and Related Functions Book in PDF, ePub and Kindle

Kamps (1995) suggested a new theoretical approach, which is called generalized order statistics (gos). This new model includes ordinary order statistics (oos), sequential order statistics, progressive type II censored order statistics and record values. The concept of gos enables a common approach to structural similarities and analogies. The distributional and inferential properties of oos and record values turn out to remain valid for gos (cf. Cramer and Kamps, 2001). Thus, the concept of gos provides a large class of models with many interesting and useful properties for both the description and the analysis of practical problems. Due to this reason, the question arises whether the general distribution theory of gos as well as their properties can be obtained by analogy with that for oos. The latter has been extensively investigated in the literature, e.g., see, David, 1981. The main purpose of this thesis is to investigate the asymptotic behavior of some important functions of gos, in view of theory of statistics and its applications. Some of these functions are non-linear, e.g., extremal product and extremal quotient and other are linear e.g., range and midrange.