Download or read book Linear Partial Differential Operators written by Lars Hörmander and published by Hassell Street Press. This book was released on 2021-09-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Download or read book Differential Equations with Operator Coefficients written by Vladimir Kozlov and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic, self-contained presentation of a theory of arbitrary order ODEs with unbounded operator coefficients in a Hilbert or Banach space. Developed over the last 10 years by the authors, it deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity.

Download or read book The Analysis of Linear Partial Differential Operators I written by Lars Hörmander and published by Springer. This book was released on 1990-08-10 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

Download or read book Transmutation and Operator Differential Equations written by and published by Elsevier. This book was released on 1979-01-01 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutation and Operator Differential Equations

Download or read book Linear Differential Operators written by Cornelius Lanczos and published by Courier Corporation. This book was released on 1997-01-01 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic and characteristic properties of linear differential operators are explored in this graduate-level text. No specific knowledge beyond the usual introductory courses is necessary. Includes 350 problems and solution.

Download or read book Exponentially Convergent Algorithms for Abstract Differential Equations written by Ivan Gavrilyuk and published by Springer Science & Business Media. This book was released on 2011-07-17 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients. For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems.

Download or read book Differential Equations with Operator Coefficients written by Kozlov, V and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Singular Ordinary Differential Operators and Pseudodifferential Equations written by Johannes Elschner and published by Springer. This book was released on 2006-11-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solving Linear Partial Differential Equations Spectra written by Martin Schechter and published by World Scientific. This book was released on 2020-06-16 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'This booklet provides a very lucid and versatile introduction to the methods of linear partial differential equations. It covers a wealth of very important material in a concise, nevertheless very instructive manner, and as such it may serve as an excellent guide to further, more advanced and detailed reading in this area of both classical and contemporary mathematics.'zbMATHPartial differential equations arise in many branches of science and they vary in many ways. No one method can be used to solve all of them, and only a small percentage have been solved. This book examines the general linear partial differential equation of arbitrary order m. Even this involves more methods than are known. We ask a simple question: when can an equation be solved and how many solutions does it have?The answer is surprising even for equations with constant coefficients. We begin with these equations, first finding conditions which allow one to solve and obtain a finite number of solutions. It is then shown how to obtain those solutions by analyzing the structure of the equation very carefully. A substantial part of the book is devoted to this. Then we tackle the more difficult problem of considering equations with variable coefficients. A large number of such equations are solved by comparing them to equations with constant coefficients.In numerous applications in the sciences, students and researchers are required to solve such equations in order to get the answers that they need. In many cases, the basic scientific theory requires the resulting partial differential equation to have a solution, and one is required to know how many solutions exist. This book deals with such situations.

Download or read book Topics in Differential and Integral Equations and Operator Theory written by Krein and published by Birkhäuser. This book was released on 2013-11-22 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume three important papers of M.G. Krein appear for the first time in English translation. Each of them is a short self-contained monograph, each a masterpiece of exposition. Although two of them were written more than twenty years ago, the passage of time has not decreased their value. They are as fresh and vital as if they had been written only yesterday. These papers contain a wealth of ideas, and will serve as a source of stimulation and inspiration for experts and beginners alike. The first paper is dedicated to the theory of canonical linear differential equations, with periodic coefficients. It focuses on the study of linear Hamiltonian systems with bounded solutions which stay bounded under small perturbations of the system. The paper uses methods from operator theory in finite and infinite dimensional spaces and complex analysis. For an account of more recent literature which was generated by this paper see AMS Translations (2), Volume 93, 1970, pages 103-176 and Integral Equations and Operator Theory, Volume 5, Number 5, 1982, pages 718-757.

Download or read book Operator Methods in Ordinary and Partial Differential Equations written by Sofʹi︠a︡ Vasilʹevna Kovalevskai︠a︡ and published by Springer Science & Business Media. This book was released on 2002 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: CO«i»b.H BaCHJIbeBHa lU>BaJIeBcR8JI (Sonja Kovalevsky) was born in Moscow in 1850 and died in Stockholm in 1891. Between these years, in the then changing and turbulent circumstances for Europe, lies the all too brief life of this remarkable woman. This life was lived out within the great European centers of power and learning in Russia, France, Germany, Switzerland, England and Sweden. To this day, now 150 years after her birth, her influence for and contribution to mathe matics, science, literature, women's rights and democratic government are recorded and reviewed, not only in Europe but now in countries far removed in time and distance from the lands of her birth and being. This volume, dedicated to her memory and to her achievements, records the Proceedings of the Marcus Wallenberg Symposium held, in memory of Sonja Kovalevsky, at Stockholm University from 18 to 22 June 2000. The symposium was held at the Department of Mathematics with its excellent library and lecture halls providing favourable working conditions. Within these pages are contained a curriculum vitae for Sonja Kovalevsky, a list of all her scientific publications, together with a copy of the moving and elegant obituary notice written by her friend and protector Gosta Mittag-Leffler. These papers are followed by a leading article entitled Sonja Kovalevsky: Her life and professorship in Stockholm, written especially for this volume by Jan-Erik Bjork in preparation for his major address to the Symposium.

Download or read book On the Asymptotic Behaviour of Solutions of Ordinary Differential Equations with Operator Coefficients VII written by V. A. Kozlov and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Partial Differential Equations with Constant Coefficients written by Francois Treves and published by CRC Press. This book was released on 1966 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Existence and approximation theorems for general differential operators -- General L2 estimates -- Fundamental solutions -- The approximation theorem -- Existence theorems for differential operators with constant coefficients -- Convexity with respect to a differential polynomial -- Interior regularity of solutions -- Partial hypoellipticity -- Existence and approximation theorems in spaces of analytic functions -- Appendix A. Semi-algebraic sets -- Appendix B. On uniqueness in the Cauchy problem -- Appendix C. Some formulas of non-commutative algebra.

Download or read book Linear Partial Differential Operators written by Lars Hörmander and published by Springer. This book was released on 2013-11-11 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Asymptotic Behaviour of Solutions of Ordinary Differential Equations with Operator Coefficients written by Vladimir A. Kozlov and published by . This book was released on 1992 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Theory of Ordinary Differential Operators written by Joachim Weidmann and published by Lecture Notes in Mathematics. This book was released on 1987-05-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.

Download or read book Functional Differential Operators and Equations written by U.G. Kurbatov and published by Springer Science & Business Media. This book was released on 1999-04-30 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with linear functional differential equations and operator theory methods for their investigation. The main topics are: the equivalence of the input-output stability of the equation Lx = &mathsf; and the invertibility of the operator L in the class of casual operators; the equivalence of input-output and exponential stability; the equivalence of the dichotomy of solutions for the homogeneous equation Lx = 0 and the invertibility of the operator L; the properties of Green's function; the independence of the stability of an equation from the norm on the space of solutions; shift invariant functional differential equations in Banach space; the possibility of the reduction of an equation of neutral type to an equation of retarded type; special full subalgebras of integral and difference operators, and operators with unbounded memory; and the analogue of Fredholm's alternative for operators with almost periodic coefficients where one-sided invertibility implies two-sided invertibility. Audience: This monograph will be of interest to students and researchers working in functional differential equations and operator theory and is recommended for graduate level courses.