Ordinary Differential Operators
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Spectral Theory Of Ordinary Differential Operators
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Author : Joachim Weidmann
language : en
Publisher: Springer
Release Date : 2006-11-15
Spectral Theory Of Ordinary Differential Operators written by Joachim Weidmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Linear Differential Operators
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Author : Cornelius Lanczos
language : en
Publisher: Courier Corporation
Release Date : 1997-01-01
Linear Differential Operators written by Cornelius Lanczos and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
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.
Ordinary Differential Operators
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Author : Aiping Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-08
Ordinary Differential Operators written by Aiping Wang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-08 with Education categories.
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.
Singular Ordinary Differential Operators And Pseudodifferential Equations
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Author : Johannes Elschner
language : en
Publisher: Springer
Release Date : 2006-11-14
Singular Ordinary Differential Operators And Pseudodifferential Equations written by Johannes Elschner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Completeness Of Root Functions Of Regular Differential Operators
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Author : Sasun Yakubov
language : en
Publisher: CRC Press
Release Date : 1993-12-20
Completeness Of Root Functions Of Regular Differential Operators written by Sasun Yakubov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-20 with Mathematics categories.
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.
Fundamental Solutions For Differential Operators And Applications
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Author : Prem Kythe
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-07-30
Fundamental Solutions For Differential Operators And Applications written by Prem Kythe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-30 with Mathematics categories.
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.
Ordinary Differential Equations
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Author : Wolfgang Walter
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-11
Ordinary Differential Equations written by Wolfgang Walter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-11 with Mathematics categories.
Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.
Linear Differential Operators Elementary Theory Of Linear Differential Operators
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Author : Mark Aronovich Naĭmark
language : en
Publisher:
Release Date : 1967
Linear Differential Operators Elementary Theory Of Linear Differential Operators written by Mark Aronovich Naĭmark and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Differential equations, Linear categories.
Ordinary Differential Equations
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Author : Refaat El Attar
language : en
Publisher: Lulu.com
Release Date : 2005-06-03
Ordinary Differential Equations written by Refaat El Attar and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-03 with Mathematics categories.
An extended introduction to ordinary differential equations. This book can be used as self study material. It contains a little bit of theory and lot of solved examples as well as tons of exercises to test your ability to solve problems using the techniques presented in the text.
Ordinary Differential Equations With Applications
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Author : Ali Mason
language : en
Publisher: Scientific e-Resources
Release Date : 2018-10-20
Ordinary Differential Equations With Applications written by Ali Mason and has been published by Scientific e-Resources this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-20 with categories.
Ordinary differential equations (ODEs) arise in many contexts of mathematics and science (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations. Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. Systems of differential equations form the basis of mathematical models in a wide range of fields - from engineering and physical sciences to finance and biological sciences. Differential equations are relations between unknown functions and their derivatives. Computing numerical solutions to differential equations is one of the most important tasks in technical computing, and one of the strengths of MATLAB. The book explains the origins of various types of differential equations. The scope of the book is limited to linear differential equations of the first order, linear differential equation of higher order, partial differential equations and special methods of solution of differential equations of second order, keeping in view the requirement of students.