Download or read book Error Inequalities in Polynomial Interpolation and Their Applications written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which presents the cumulation of the authors' research in the field, deals with Lidstone, Hermite, Abel--Gontscharoff, Birkhoff, piecewise Hermite and Lidstone, spline and Lidstone--spline interpolating problems. Explicit representations of the interpolating polynomials and associated error functions are given, as well as explicit error inequalities in various norms. Numerical illustrations are provided of the importance and sharpness of the various results obtained. Also demonstrated are the significance of these results in the theory of ordinary differential equations such as maximum principles, boundary value problems, oscillation theory, disconjugacy and disfocality. For mathematicians, numerical analysts, computer scientists and engineers.
Download or read book Progress on Difference Equations and Discrete Dynamical Systems written by Steve Baigent and published by Springer Nature. This book was released on 2021-01-04 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises selected papers of the 25th International Conference on Difference Equations and Applications, ICDEA 2019, held at UCL, London, UK, in June 2019. The volume details the latest research on difference equations and discrete dynamical systems, and their application to areas such as biology, economics, and the social sciences. Some chapters have a tutorial style and cover the history and more recent developments for a particular topic, such as chaos, bifurcation theory, monotone dynamics, and global stability. Other chapters cover the latest personal research contributions of the author(s) in their particular area of expertise and range from the more technical articles on abstract systems to those that discuss the application of difference equations to real-world problems. The book is of interest to both Ph.D. students and researchers alike who wish to keep abreast of the latest developments in difference equations and discrete dynamical systems.
Download or read book Advanced Inequalities written by George A Anastassiou and published by World Scientific. This book was released on 2010-10-26 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end.The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy-Opial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as Chebyshev-Gruss, Gruss and Comparison of Means inequalities are studied.The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.
Download or read book Trends and Applications in Constructive Approximation written by Detlef H. Mache and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.
Download or read book Approximation Theory written by Narenda Govil and published by CRC Press. This book was released on 2021-02-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."
Download or read book Integration on Infinite Dimensional Surfaces and Its Applications written by A. V. Uglanov and published by Springer Science & Business Media. This book was released on 2000-01-31 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of integration over surfaces in abstract topological vector space. Applications of the theory in different fields, such as infinite dimensional distributions and differential equations (including boundary value problems), stochastic processes, approximation of functions, and calculus of variation on a Banach space, are treated in detail. Audience: This book will be of interest to specialists in functional analysis, and those whose work involves measure and integration, probability theory and stochastic processes, partial differential equations and mathematical physics.
Download or read book Recent Progress in Inequalities written by G.V. Milovanovic and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.
Download or read book Elimination Methods in Polynomial Computer Algebra written by V. Bykov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is connected with a new direction in mathematics, which has been actively developed over the last few years, namely the field of polynomial computer algebra, which lies at the intersection point of algebra, mathematical analysis and programming. There were several incentives to write the book. First of all, there has lately been a considerable interest in applied nonlinear problems characterized by multiple sta tionary states. Practical needs have then in their turn led to the appearance of new theoretical results in the analysis of systems of nonlinear algebraic equations. And finally, the introduction of various computer packages for analytic manipulations has made it possible to use complicated elimination-theoretical algorithms in prac tical research. The structure of the book is accordingly represented by three main parts: Mathematical results driven to constructive algorithms, computer algebra realizations of these algorithms, and applications. Nonlinear systems of algebraic equations arise in diverse fields of science. In particular, for processes described by systems of differential equations with a poly nomial right hand side one is faced with the problem of determining the number (and location) of the stationary states in certain sets.
Download or read book Modern Umbral Calculus written by Francesco Aldo Costabile and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel approach to umbral calculus, which uses only elementary linear algebra (matrix calculus) based on the observation that there is an isomorphism between Sheffer polynomials and Riordan matrices, and that Sheffer polynomials can be expressed in terms of determinants. Additionally, applications to linear interpolation and operator approximation theory are presented in many settings related to various families of polynomials.
Download or read book Applications of Point Set Theory in Real Analysis written by A.B. Kharazishvili and published by Springer Science & Business Media. This book was released on 1998-03-31 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to some results from the classical Point Set Theory and their applications to certain problems in mathematical analysis of the real line. Notice that various topics from this theory are presented in several books and surveys. From among the most important works devoted to Point Set Theory, let us first of all mention the excellent book by Oxtoby [83] in which a deep analogy between measure and category is discussed in detail. Further, an interesting general approach to problems concerning measure and category is developed in the well-known monograph by Morgan [79] where a fundamental concept of a category base is introduced and investigated. We also wish to mention that the monograph by Cichon, W«;glorz and the author [19] has recently been published. In that book, certain classes of subsets of the real line are studied and various cardinal valued functions (characteristics) closely connected with those classes are investigated. Obviously, the IT-ideal of all Lebesgue measure zero subsets of the real line and the IT-ideal of all first category subsets of the same line are extensively studied in [19], and several relatively new results concerning this topic are presented. Finally, it is reasonable to notice here that some special sets of points, the so-called singular spaces, are considered in the classi
Download or read book The Analysis of Solutions of Elliptic Equations written by Nikolai Tarkhanov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat- faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications. We consider, as a rule, differential operators having a simple structure on open subsets of Rn. Currently, this area is not being investigated very actively, possibly because it is already very highly developed actively (cf. for example the book of Palamodov [213]). However, even in this (well studied) situation the general ideas from [291] allow us to obtain new results in the qualitative theory of differential equations and frequently in definitive form. The greater part of the material presented is related to applications of the L- rent series for a solution of a system of differential equations, which is a convenient way of writing the Green formula. The culminating application is an analog of the theorem of Vitushkin [303] for uniform and mean approximation by solutions of an elliptic system. Somewhat afield are several questions on ill-posedness, but the parametrix method enables us to obtain here a series of hitherto unknown facts.
Download or read book Trigonometric Fourier Series and Their Conjugates written by L. Zhizhiashvili and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates.
Download or read book Focal Boundary Value Problems for Differential and Difference Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations. In this vast field of research, the conjugate (Hermite) and the right focal point (Abei) types of problems have received the maximum attention. This is largely due to the fact that these types of problems are basic, in the sense that the methods employed in their study are easily extendable to other types of prob lems. Moreover, the conjugate and the right focal point types of boundary value problems occur frequently in real world problems. In the monograph Boundary Value Problems for Higher Order Differential Equations published in 1986, we addressed the theory of conjugate boundary value problems. At that time the results on right focal point problems were scarce; however, in the last ten years extensive research has been done. In Chapter 1 of the mono graph we offer up-to-date information of this newly developed theory of right focal point boundary value problems. Until twenty years ago Difference Equations were considered as the dis cretizations of the differential equations. Further, it was tacitly taken for granted that the theories of difference and differential equations are parallel. However, striking diversities and wide applications reported in the last two decades have made difference equations one of the major areas of research.
Download or read book A Course in Approximation Theory written by Elliott Ward Cheney and published by American Mathematical Soc.. This book was released on 2009-01-13 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.
Download or read book Boundary Value Problems in the Spaces of Distributions written by Y. Roitberg and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents elliptic, parabolic and hyperbolic boundary value problems for systems of mixed orders (Douglis-Nirenberg systems). For these problems the `theorem on complete collection of isomorphisms' is proven. Several applications in elasticity and hydrodynamics are treated. The book requires familiarity with the elements of functional analysis, the theory of partial differential equations, and the theory of generalized functions. Audience: This work will be of interest to graduate students and research mathematicians involved in areas such as functional analysis, partial differential equations, operator theory, the mathematics of mechanics, elasticity and viscoelasticity.
Download or read book Elliptic Boundary Value Problems in the Spaces of Distributions written by Y. Roitberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume endeavours to summarise all available data on the theorems on isomorphisms and their ever increasing number of possible applications. It deals with the theory of solvability in generalised functions of general boundary-value problems for elliptic equations. In the early sixties, Lions and Magenes, and Berezansky, Krein and Roitberg established the theorems on complete collection of isomorphisms. Further progress of the theory was connected with proving the theorem on complete collection of isomorphisms for new classes of problems, and hence with the development of new methods to prove these theorems. The theorems on isomorphisms were first established for elliptic equations with normal boundary conditions. However, after the Noetherian property of elliptic problems was proved without assuming the normality of the boundary expressions, this became the natural way to consider the problems of establishing the theorems on isomorphisms for general elliptic problems. The present author's method of solving this problem enabled proof of the theorem on complete collection of isomorphisms for the operators generated by elliptic boundary-value problems for general systems of equations. Audience: This monograph will be of interest to mathematicians whose work involves partial differential equations, functional analysis, operator theory and the mathematics of mechanics.
Download or read book The Gibbs Phenomenon in Fourier Analysis Splines and Wavelet Approximations written by A.J. Jerri and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the first attempt at a unified picture for the pres ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In ad dition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximation, and continuous as well as discrete wavelet approximations. The mate rial in this book is presented in a manner accessible to upperclassmen and graduate students in science and engineering, as well as researchers who may face the Gibbs phenomenon in the varied applications that in volve the Fourier and the other approximations of functions with jump discontinuities. Those with more advanced backgrounds in analysis will find basic material, results, and motivations from which they can begin to develop deeper and more general results. We must emphasize that the aim of this book (the first on the sUbject): to satisfy such a diverse audience, is quite difficult. In particular, our detailed derivations and their illustrations for an introductory book may very well sound repeti tive to the experts in the field who are expecting a research monograph. To answer the concern of the researchers, we can only hope that this book will prove helpful as a basic reference for their research papers.
