Complete Second Order Linear Differential Equations In Hilbert Spaces
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Complete Second Order Linear Differential Equations In Hilbert Spaces
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Author : Alexander Ya. Shklyar
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Complete Second Order Linear Differential Equations In Hilbert Spaces written by Alexander Ya. Shklyar and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. This monograph is an attempt to present a unified systematic theory of second order equations y" (t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy problem as well as the Dirichlet and Neumann problems. Exhaustive yet clear answers to all posed questions are given. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations. For this purpose, some new results in the spectral theory of pairs of operators and the boundary behavior of integral transforms have been developed. The book serves as a self-contained introductory course and a reference book on this subject for undergraduate and post- graduate students and research mathematicians in analysis. Moreover, users will welcome having a comprehensive study of the equations at hand, and it gives insight into the theory of complete second order linear differential equations in a general context - a theory which is far from being fully understood.
Second Order Partial Differential Equations In Hilbert Spaces
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Author : Giuseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 2002-07-25
Second Order Partial Differential Equations In Hilbert Spaces written by Giuseppe Da Prato and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-25 with Mathematics categories.
State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.
Tests For Correctness And Weak Correctness Of The Couchy Problem For Complete Second Order Linear Differential Equations In Hilbert Spaces
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Author : Aleksandr Jakovlevič Škljar
language : en
Publisher:
Release Date : 1993
Tests For Correctness And Weak Correctness Of The Couchy Problem For Complete Second Order Linear Differential Equations In Hilbert Spaces written by Aleksandr Jakovlevič Škljar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Tests For Correctness And Weak Correctness Of The Cauchy Problem For Complete Second Order Linear Differential Equations In Hilbert Spaces
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Author : A. Ya Shklyar
language : en
Publisher:
Release Date : 1993
Tests For Correctness And Weak Correctness Of The Cauchy Problem For Complete Second Order Linear Differential Equations In Hilbert Spaces written by A. Ya Shklyar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Second Order Linear Differential Equations In Banach Spaces
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Author : H.O. Fattorini
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Second Order Linear Differential Equations In Banach Spaces written by H.O. Fattorini and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.
Nonlinear Evolution And Difference Equations Of Monotone Type In Hilbert Spaces
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Author : Behzad Djafari Rouhani
language : en
Publisher: CRC Press
Release Date : 2019-05-20
Nonlinear Evolution And Difference Equations Of Monotone Type In Hilbert Spaces written by Behzad Djafari Rouhani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-20 with Mathematics categories.
This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator. This class of abstract evolution equations contains ordinary differential equations, as well as the unification of some important partial differential equations including heat equation, wave equation, Schrodinger equation, etc. The book contains a collection of the authors' work and applications in this field, as well as those of other authors.
Differential Equations Fourier Series And Hilbert Spaces
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Author : Raffaele Chiappinelli
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-09-18
Differential Equations Fourier Series And Hilbert Spaces written by Raffaele Chiappinelli and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-18 with Mathematics categories.
This book is intended to be used as a rather informal, and surely not complete, textbook on the subjects indicated in the title. It collects my Lecture Notes held during three academic years at the University of Siena for a one semester course on "Basic Mathematical Physics", and is organized as a short presentation of few important points on the arguments indicated in the title. It aims at completing the students' basic knowledge on Ordinary Differential Equations (ODE) - dealing in particular with those of higher order - and at providing an elementary presentation of the Partial Differential Equations (PDE) of Mathematical Physics, by means of the classical methods of separation of variables and Fourier series. For a reasonable and consistent discussion of the latter argument, some elementary results on Hilbert spaces and series expansion in othonormal vectors are treated with some detail in Chapter 2. Prerequisites for a satisfactory reading of the present Notes are not only a course of Calculus for functions of one or several variables, but also a course in Mathematical Analysis where - among others - some basic knowledge of the topology of normed spaces is supposed to be included. For the reader's convenience some notions in this context are explicitly recalled here and there, and in particular as an Appendix in Section 1.4. An excellent reference for this general background material is W. Rudin's classic Principles of Mathematical Analysis. On the other hand, a complete discussion of the results on ODE and PDE that are here just sketched are to be found in other books, specifically and more deeply devoted to these subjects, some of which are listed in the Bibliography. In conclusion and in brief, my hope is that the present Notes can serve as a second quick reading on the theme of ODE, and as a first introductory reading on Fourier series, Hilbert spaces, and PDE
Applied Analysis By The Hilbert Space Method
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Author : Samuel S. Holland
language : en
Publisher: Courier Corporation
Release Date : 2007-06-05
Applied Analysis By The Hilbert Space Method written by Samuel S. Holland and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-05 with Mathematics categories.
Numerous worked examples and exercises highlight this unified treatment of the Hermitian operator theory in its Hilbert space setting. Its simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. Featuring full discussions of first and second order linear differential equations, the text introduces the fundamentals of Hilbert space theory and Hermitian differential operators. It derives the eigenvalues and eigenfunctions of classical Hermitian differential operators, develops the general theory of orthogonal bases in Hilbert space, and offers a comprehensive account of Schrödinger's equations. In addition, it surveys the Fourier transform as a unitary operator and demonstrates the use of various differentiation and integration techniques. Samuel S. Holland, Jr. is a professor of mathematics at the University of Massachusetts, Amherst. He has kept this text accessible to undergraduates by omitting proofs of some theorems but maintaining the core ideas of crucially important results. Intuitively appealing to students in applied mathematics, physics, and engineering, this volume is also a fine reference for applied mathematicians, physicists, and theoretical engineers.
The Cauchy Problem For Higher Order Abstract Differential Equations
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Author : Ti-Jun Xiao
language : en
Publisher: Springer
Release Date : 2013-12-11
The Cauchy Problem For Higher Order Abstract Differential Equations written by Ti-Jun Xiao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.
Hilbert Space Boundary Value Problems And Orthogonal Polynomials
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Author : Allan M. Krall
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Hilbert Space Boundary Value Problems And Orthogonal Polynomials written by Allan M. Krall 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 2002 with Mathematics categories.
This monograph consists of three parts: - the abstract theory of Hilbert spaces, leading up to the spectral theory of unbounded self-adjoined operators; - the application to linear Hamiltonian systems, giving the details of the spectral resolution; - further applications such as to orthogonal polynomials and Sobolev differential operators. Written in textbook style this up-to-date volume is geared towards graduate and postgraduate students and researchers interested in boundary value problems of linear differential equations or in orthogonal polynomials.