Differential Equations With Operator Coefficients

DOWNLOAD

Download Differential Equations With Operator Coefficients PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Differential Equations With Operator Coefficients book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Differential Equations With Operator Coefficients

DOWNLOAD
Author : Vladimir Kozlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Differential Equations With Operator Coefficients written by Vladimir Kozlov 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 2013-04-18 with Mathematics categories.

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.

Differential Equations With Operator Coefficients

DOWNLOAD
Author : Kozlov, V
language : en
Publisher:
Release Date : 1999

Differential Equations With Operator Coefficients written by Kozlov, V and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

Homogenization Of Differential Operators And Integral Functionals

DOWNLOAD
Author : V.V. Jikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Homogenization Of Differential Operators And Integral Functionals written by V.V. Jikov 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 2012-12-06 with Mathematics categories.

It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

Spectral Theory Of Ordinary Differential Operators

DOWNLOAD
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.

Boundary Value Problems For Operator Differential Equations

DOWNLOAD
Author : Myroslav L. Gorbachuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Boundary Value Problems For Operator Differential Equations written by Myroslav L. Gorbachuk 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 2012-12-06 with Mathematics categories.

Transmutation And Operator Differential Equations

DOWNLOAD
Author :
language : en
Publisher: Elsevier
Release Date : 1979-01-01

Transmutation And Operator Differential Equations written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-01-01 with Mathematics categories.

Transmutation and Operator Differential Equations

Floquet Theory For Partial Differential Equations

DOWNLOAD
Author : P.A. Kuchment
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-07-01

Floquet Theory For Partial Differential Equations written by P.A. Kuchment 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 1993-07-01 with Science categories.

Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].

Linear Sobolev Type Equations And Degenerate Semigroups Of Operators

DOWNLOAD
Author : G. A. Sviridyuk
language : en
Publisher:
Release Date : 2003

Linear Sobolev Type Equations And Degenerate Semigroups Of Operators written by G. A. Sviridyuk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Partial Differential Equations Vii

DOWNLOAD
Author : M.A. Shubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Partial Differential Equations Vii written by M.A. Shubin 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 2013-03-09 with Mathematics categories.

§18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrödinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 §19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 §20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20.5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera tor. In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series.

Differential Operator Equations

DOWNLOAD
Author : Yakov Yakubov
language : en
Publisher: CRC Press
Release Date : 1999-11-24

Differential Operator Equations written by Yakov 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 1999-11-24 with Mathematics categories.

The theory of differential-operator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics. Although a number of published works address differential-operator equations of the first and second orders, to date none offer a treatment of the higher orders. In Differential-Operator Equations, the authors present a systematic treatment of the theory of differential-operator equations of higher order, with applications to partial differential equations. They construct a theory that allows application to both regular and irregular differential problems. In particular, they study problems that cannot be solved by various known methods and irregular problems not addressed in existing monographs. These include Birkhoff-irregularity, non-local boundary value conditions, and non-smoothness of the boundary of the domains. Among this volume's other points of interest are: The Abel basis property of a system of root functions Irregular boundary value problems The theory of hyperbolic equations in Gevrey space The theory of boundary value problems for elliptic differential equations with a parameter