Ordinary Differential Operators PDF Download
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Author | : Prem Kythe |
Publisher | : Springer Science & Business Media |
Total Pages | : 448 |
Release | : 1996-07-30 |
Genre | : Mathematics |
ISBN | : 9780817638696 |
Download Fundamental Solutions for Differential Operators and Applications Book in PDF, ePub and Kindle
A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects.
Author | : Joachim Weidmann |
Publisher | : Springer |
Total Pages | : 310 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540479120 |
Download Spectral Theory of Ordinary Differential Operators Book in PDF, ePub and Kindle
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.
Author | : Cornelius Lanczos |
Publisher | : SIAM |
Total Pages | : 581 |
Release | : 1997-12-01 |
Genre | : Mathematics |
ISBN | : 9781611971187 |
Download Linear Differential Operators Book in PDF, ePub and Kindle
Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems. Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: "What are the basic and characteristic properties of linear differential operators?" In the author's words, this book is written for those "to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field."
Author | : Cornelius Lanczos |
Publisher | : Courier Corporation |
Total Pages | : 604 |
Release | : 1997-01-01 |
Genre | : Mathematics |
ISBN | : 9780486680354 |
Download Linear Differential Operators Book in PDF, ePub and Kindle
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.
Author | : Aiping Wang |
Publisher | : American Mathematical Soc. |
Total Pages | : 250 |
Release | : 2019-11-08 |
Genre | : Education |
ISBN | : 1470453665 |
Download Ordinary Differential Operators Book in PDF, ePub and Kindle
In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
Author | : Sasun Yakubov |
Publisher | : CRC Press |
Total Pages | : 276 |
Release | : 1993-12-20 |
Genre | : Mathematics |
ISBN | : 9780582236929 |
Download Completeness of Root Functions of Regular Differential Operators Book in PDF, ePub and Kindle
The precise mathematical investigation of various natural phenomena is an old and difficult problem. This book is the first to deal systematically with the general non-selfadjoint problems in mechanics and physics. It deals mainly with bounded domains with smooth boundaries, but also considers elliptic boundary value problems in tube domains, i.e. in non-smooth domains. This volume will be of particular value to those working in differential equations, functional analysis, and equations of mathematical physics.
Author | : Earl A. Coddington |
Publisher | : |
Total Pages | : 292 |
Release | : 1968 |
Genre | : Differential equations |
ISBN | : |
Download An Introduction to Ordinary Differential Equations Book in PDF, ePub and Kindle
Author | : Johannes Elschner |
Publisher | : Springer |
Total Pages | : 199 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540392947 |
Download Singular Ordinary Differential Operators and Pseudodifferential Equations Book in PDF, ePub and Kindle
Author | : Randall J. LeVeque |
Publisher | : SIAM |
Total Pages | : 356 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 9780898717839 |
Download Finite Difference Methods for Ordinary and Partial Differential Equations Book in PDF, ePub and Kindle
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Author | : Viktor Pavlovich Palamodov |
Publisher | : Springer |
Total Pages | : 464 |
Release | : 1970 |
Genre | : Mathematics |
ISBN | : |
Download Linear Differential Operators with Constant Coefficients Book in PDF, ePub and Kindle
This book contains a systematic exposition of the facts relating to partial differential equations with constant coefficients. The study of systems of equations in general form occupies a central place. Together with the classical problems of the existence, the uniqueness, and the regularity of the solutions, we also consider the specific problems that arise in connection with overdetermined and underdetermined systems of equations: the extendabiIity of the solutions into a wider region, the extendability of regularity, M-cohomology and so on. Great attention is paid to the connections and the parallels with the theory of functions of several complex variables. The choice of material was dictated by a number of considerations. Among all the facts relating to general systems of equations, the book contains none that relate to the behavior of differential operators in spaces of slowly growing functions. Missing also are results relating to a single equation in one unknown function: the correctness of the Cauchy problem, certain theorems on p-convexity, and the theory of boundary values, are all set forth in other monographs (Gel'fand and Silov [3], Hormander [10] and Treves [4]). The book consists of two parts. In the first, we set forth the analytic method which forms the basis for the contents of the second part, which itself is dedicated to differential equations. The first part is pre ceded by an introduction in which the content and methods of Part I are described. All the notes and bibliographical references are collected together in a special section.