Download or read book Spectral Theory of Approximation Methods for Convolution Equations written by Roland Hagen and published by Birkhäuser. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.

Download or read book Approximation of Additive Convolution Like Operators written by Victor Didenko and published by Springer Science & Business Media. This book was released on 2008-09-19 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The list of the methods considered includes spline Galerkin, spline collocation, qualocation, and quadrature methods. The book is self-contained and accessible to graduate students.

Download or read book Recent Developments in Operator Theory and Its Applications written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers selected for publication here, many of them written by leaders in the field, bring readers up to date on recent achievements in modern operator theory and applications. The book’s subject matter is of practical use to a wide audience in mathematical and engineering sciences.

Download or read book Ordinary Differential Equations and Integral Equations written by C.T.H. Baker and published by Elsevier. This book was released on 2001-06-20 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! This volume contains contributions in the area of differential equations and integral equations. Many numerical methods have arisen in response to the need to solve "real-life" problems in applied mathematics, in particular problems that do not have a closed-form solution. Contributions on both initial-value problems and boundary-value problems in ordinary differential equations appear in this volume. Numerical methods for initial-value problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (one-step methods) and those which are based on several values of the solution (multistep methods).John Butcher has supplied an expert's perspective of the development of numerical methods for ordinary differential equations in the 20th century. Rob Corless and Lawrence Shampine talk about established technology, namely software for initial-value problems using Runge-Kutta and Rosenbrock methods, with interpolants to fill in the solution between mesh-points, but the 'slant' is new - based on the question, "How should such software integrate into the current generation of Problem Solving Environments?"Natalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the nth power of square matrices.The dynamical system viewpoint has been of great benefit to ODE theory and numerical methods. Related is the study of chaotic behaviour.Willy Govaerts discusses the numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems.Arieh Iserles and Antonella Zanna survey the construction of Runge-Kutta methods which preserve algebraic invariant functions.Valeria Antohe and Ian Gladwell present numerical experiments on solving a Hamiltonian system of Hénon and Heiles with a symplectic and a nonsymplectic method with a variety of precisions and initial conditions.Stiff differential equations first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on A-stable multistep methods and Butcher's first paper on implicit Runge-Kutta methods.Ernst Hairer and Gerhard Wanner deliver a survey which retraces the discovery of the order stars as well as the principal achievements obtained by that theory.Guido Vanden Berghe, Hans De Meyer, Marnix Van Daele and Tanja Van Hecke construct exponentially fitted Runge-Kutta methods with s stages.Differential-algebraic equations arise in control, in modelling of mechanical systems and in many other fields.Jeff Cash describes a fairly recent class of formulae for the numerical solution of initial-value problems for stiff and differential-algebraic systems.Shengtai Li and Linda Petzold describe methods and software for sensitivity analysis of solutions of DAE initial-value problems.Again in the area of differential-algebraic systems, Neil Biehn, John Betts, Stephen Campbell and William Huffman present current work on mesh adaptation for DAE two-point boundary-value problems.Contrasting approaches to the question of how good an approximation is as a solution of a given equation involve (i) attempting to estimate the actual error (i.e., the difference between the true and the approximate solutions) and (ii) attempting to estimate the defect - the amount by which the approximation fails to satisfy the given equation and any side-conditions.The paper by Wayne Enright on defect control relates to carefully analyzed techniques that have been proposed both for ordinary differential equations and for delay differential equations in which an attempt is made to control an estimate of the size of the defect.Many phenomena incorporate noise, and the numerical solution of

Download or read book Boundary Elements Implementation and Analysis of Advanced Algorithms written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Englischer Text: The volume contains 21 contributions to the 12th GAMM-Seminar (Kiel, January 1996), which was devoted to advanced algorithms in the field of boundary element methods. The topics were e. g. cubature techniques, multiscale methods, hp-discretisation, error estimation, domain decomposition, and programm design. Deutscher Text: Der Band enthält die 21 Beiträge zum 12. GAMM-Seminar (Kiel, Jaunuar 1996), welches sich mit fortgeschrittenen Algorithmen auf dem Gebiet der Randwertprobleme befaßte.

Download or read book The Maz ya Anniversary Collection written by Jürgen Rossmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the week of August 31 - September 4, 1998, a conference in honour of Vladimir Maz'ya was held in Rostock as a satellite meeting of the World Congress of Mathematicians. It was sponsored by the German Research Founda tion (Deutsche Forschungsgemeinschaft) and the Ministry of Education and Cul tural Affairs of the land Mecklenburg-Vorpommern. During his forty year career Maz'ya contributed to so many areas of mathematical analysis that such a broad topic of the conference as "Functional Analysis, Partial Differential Equations and Applications" sounds quite nat~al. The conference was organized by the Depart ment of Mathematics of the University of Rostock and the Weierstrass Institute of Applied Analysis and Stochastics in Berlin on the occasion of his 60th birth day. For many years Maz'ya was connected with mathematicians from Berlin and Rostock through his work in potential theory, in differential and pseudodifferen tial equations and in approximation theory. In 1990 he was awarded an honorary doctorate by the University of Rostock. Shortly before the meeting, one of its organizers, an outstanding mathematician and Maz'ya's dear friend, Siegfried Pr6Bdorf died. This was a heavy loss for the and for the conference in particular. During the German mathematical community meeting the rector of the University of Rostock, Prof. Wildenhain, the director of the Weierstrass Institute, Prof. Sprekels, and Prof. Maz'ya remembered S. Pr6Bdorf very warmly. The conference was attended by 109 mathematicians from 21 countries, and the program included 24 invited lectures and 63 short communications.

Download or read book Toeplitz Matrices and Singular Integral Equations written by Albrecht Böttcher and published by Birkhäuser. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts. The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications. The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory.

Download or read book Singular Integral Operators Factorization and Applications written by Albrecht Böttcher and published by Birkhäuser. This book was released on 2012-12-06 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Workshop on Operator Theory and Applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were !> Factorization Theory; !> Factorization and Integrable Systems; !> Operator Theoretical Methods in Diffraction Theory; !> Algebraic Techniques in Operator Theory; !> Applications to Mathematical Physics and Related Topics. A total of 94 colleagues from 21 countries participated in the conference. The major part of participants came from Portugal (32), Germany (17), Israel (6), Mexico (6), the Netherlands (5), USA (4) and Austria (4). The others were from Ukraine, Venezuela (3 each), Spain, Sweden (2 each), Algeria, Australia, Belorussia, France, Georgia, Italy, Japan, Kuwait, Russia and Turkey (one of each country). It was the 12th meeting in the framework of the IWOTA conferences which started in 1981 on an initiative of Professors 1. Gohberg (Tel Aviv) and J. W. Helton (San Diego). Up to now, it was the largest conference in the field of Operator Theory in Portugal.

Download or read book Problems and Methods in Mathematical Physics written by Johannes Elschner and published by Birkhäuser. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physics (11th TMP), held in Chemnitz, March 25-28, 1999. The conference was dedicated to the memory of Siegfried Prössdorf, who made important contributions to the theory and numerical analysis of operator equations and their applications in mathematical physics and mechanics. The main part of the book comprises original research papers. The topics are ranging from integral and pseudodifferential equations, boundary value problems, operator theory, boundary element and wavelet methods, approximation theory and inverse problems to various concrete problems and applications in physics and engineering, and reflect Prössdorf's broad spectrum of research activities. The volume also contains articles describing the life and mathematical achievements of Siegfried Prössdorf and includes a list of his publications. The book is addressed to a wide audience in the mathematical and engineering sciences.

Download or read book Contemporary Computational Mathematics A Celebration of the 80th Birthday of Ian Sloan written by Josef Dick and published by Springer. This book was released on 2018-05-23 with total page 1309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

Download or read book Limit Operators and Their Applications in Operator Theory written by Vladimir Rabinovich and published by Birkhäuser. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph devoted to a fairly wide class of operators, namely band and band-dominated operators and their Fredholm theory. The main tool in studying this topic is limit operators. Applications are presented to several important classes of such operators: convolution type operators and pseudo-differential operators on bad domains and with bad coefficients.

Download or read book Spectral Theory Mathematical System Theory Evolution Equations Differential and Difference Equations written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2012-06-15 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains a collection of original research articles and expository contributions on recent developments in operator theory and its multifaceted applications. They cover a wide range of themes from the IWOTA 2010 conference held at the TU Berlin, Germany, including spectral theory, function spaces, mathematical system theory, evolution equations and semigroups, and differential and difference operators. The book encompasses new trends and various modern topics in operator theory, and serves as a useful source of information to mathematicians, scientists and engineers.

Download or read book Topics in Interpolation Theory written by Bernd Fritzsche and published by Birkhäuser. This book was released on 2012-12-06 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: About one half of the papers in this volume are based on lectures which were pre sented at a conference at Leipzig University in August 1994, which was dedicated to Vladimir Petrovich Potapov. He would have been eighty years old. These have been supplemented by: (1) Historical material, based on reminiscences of former colleagues, students and associates of V.P. Potapov. (2) Translations of a number of important papers (which serve to clarify the Potapov approach to problems of interpolation and extension, as well as a number of related problems and methods) and are relatively unknown in the West. (3) Two expository papers, which have been especially written for this volume. For purposes of discussion, it is convenient to group the technical papers in this volume into six categories. We will now run through them lightly, first listing the major theme, then in parentheses the authors of the relevant papers, followed by discussion. Some supplementary references are listed at the end; OT72 which appears frequently in this volume, refers to Volume 72 in the series Operator Theory: Advances and Applications. It was dedicated to V.P. Potapov. 1. Multiplicative decompositions (Yu.P. Ginzburg; M.S. Livsic, I.V. Mikhailova; V.I. Smirnov).

Download or read book Topics In Interpolation Theory written by Harry Dym and published by Springer Science & Business Media. This book was released on 1997 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Petrovich Potapov, as remembered by colleagues, friends and former students.- On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc.- On tangential interpolation in reproducing kernel Hilbert modules and applications.- Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions.- The indefinite metric in the Schur interpolation problem for analytic functions, IV.- Bitangential interpolation for upper triangular operators.- Bitangential interpolation for upper triangular operators when the Pick operator is strictly positive.- Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class.- On recovering a multiplicative integral from its modulus.- On Schur functions and Szegö orthogonal polynomials.- Hilbert spaces of entire functions as a J theory subject.- On transformations of Potapov's fundamental matrix inequality.- An abstract interpolation problem and the extension theory of isometric operators.- On the theory of matrix-valued functions belonging to the Smirnov class.- Integral representation of function of class Ka.- On the theory of entire matrix-functions of exponential type.- Analogs of Nehari and Sarason theorems for character-automorphic functions and some related questions.- The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators.- Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner functions.- On a criterion of positive definiteness.- Matrix boundary value problems with eigenvalue dependent boundary conditions (The linear case).- Weyl-Titchmarsh functions of the canonical periodical system of differential equations.- On boundary values of functions regular in a disk.

Download or read book Integral Equations with Difference Kernels on Finite Intervals written by Lev A. Sakhnovich and published by Birkhäuser. This book was released on 2012-12-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal synthesis, light scattering, and diffraction on a ribbon are just some of the applied problems for which integral equations with difference kernels are employed. The same equations are also met in important mathematical problems such as inverse spectral problems, nonlinear integral equations, and factorization of operators. On the basis of the operator identity method, the theory of integral operators with difference kernels is developed here, and the connection with many applied and theoretical problems is studied. A number of important examples are analyzed.

Download or read book Linear Functional Equations Operator Approach written by Anatolij Antonevich and published by Birkhäuser. This book was released on 2012-12-06 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ ual representatives are related with problems arising in various areas of mathemat ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au tomorphisms of Banach algebras, and other problems.

Download or read book Measures of Noncompactness in Metric Fixed Point Theory written by J.M. Ayerbe Toledano and published by Birkhäuser. This book was released on 2012-12-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is clear and easy to grasp attracts us; complications deter David Hilbert The material presented in this volume is based on discussions conducted in peri odically held seminars by the Nonlinear Functional Analysis research group of the University of Seville. This book is mainly addressed to those working or aspiring to work in the field of measures of noncompactness and metric fixed point theory. Special em phasis is made on the results in metric fixed point theory which were derived from geometric coefficients defined by means of measures of noncompactness and on the relationships between nonlinear operators which are contractive for different measures. Several topics in these notes can be found either in texts on measures of noncompactness (see [AKPRSj, [BG]) or in books on metric fixed point theory (see [GK1], [Sm], [Z]). Many other topics have come from papers where the authors of this volume have published the results of their research over the last ten years. However, as in any work of this type, an effort has been made to revise many proofs and to place many others in a correct setting. Our research was made possible by partial support of the D.G.I.C.y'T. and the Junta de Andalucia.