Complete Second Order Linear Differential Equations In Hilbert Spaces

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Complete Second Order Linear Differential Equations in Hilbert Spaces

Alexander Ya. Shklyar
Complete Second Order Linear Differential Equations in Hilbert Spaces Book PDF

Author : Alexander Ya. Shklyar
Publisher : Birkhäuser
Page : 225 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034891875

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Complete Second Order Linear Differential Equations in Hilbert Spaces by Alexander Ya. Shklyar Pdf

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

Giuseppe Da Prato,Jerzy Zabczyk
Second Order Partial Differential Equations in Hilbert Spaces Book PDF

Author : Giuseppe Da Prato,Jerzy Zabczyk
Publisher : Cambridge University Press
Page : 397 pages
File Size : 43,9 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 9781139433433

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Second Order Partial Differential Equations in Hilbert Spaces by Giuseppe Da Prato,Jerzy Zabczyk Pdf

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.

Second Order Linear Differential Equations in Banach Spaces

H.O. Fattorini
Second Order Linear Differential Equations in Banach Spaces Book PDF

Author : H.O. Fattorini
Publisher : Elsevier
Page : 313 pages
File Size : 54,7 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080872190

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Second Order Linear Differential Equations in Banach Spaces by H.O. Fattorini Pdf

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.

Operator Theory and Its Applications

Alexander G. Ramm,P. N. Shivakumar,Abraham Vilgelmovich Strauss
Operator Theory and Its Applications Book PDF

Author : Alexander G. Ramm,P. N. Shivakumar,Abraham Vilgelmovich Strauss
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 47,9 Mb
Release : 2000
Category : Operator theory
ISBN : 9780821819906

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Operator Theory and Its Applications by Alexander G. Ramm,P. N. Shivakumar,Abraham Vilgelmovich Strauss Pdf

Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.

Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces

Behzad Djafari Rouhani
Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces Book PDF

Author : Behzad Djafari Rouhani
Publisher : CRC Press
Page : 450 pages
File Size : 44,8 Mb
Release : 2019-05-20
Category : Mathematics
ISBN : 9781482228199

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Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces by Behzad Djafari Rouhani Pdf

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.

Introduction to Partial Differential Equations and Hilbert Space Methods

Karl E. Gustafson
Introduction to Partial Differential Equations and Hilbert Space Methods Book PDF

Author : Karl E. Gustafson
Publisher : Courier Corporation
Page : 500 pages
File Size : 40,8 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486140872

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Introduction to Partial Differential Equations and Hilbert Space Methods by Karl E. Gustafson Pdf

Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.

The Cauchy Problem for Higher Order Abstract Differential Equations

Ti-Jun Xiao,Jin Liang
The Cauchy Problem for Higher Order Abstract Differential Equations Book PDF

Author : Ti-Jun Xiao,Jin Liang
Publisher : Springer
Page : 314 pages
File Size : 45,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783540494799

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The Cauchy Problem for Higher Order Abstract Differential Equations by Ti-Jun Xiao,Jin Liang Pdf

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

Allan M. Krall
Hilbert Space Boundary Value Problems and Orthogonal Polynomials Book PDF

Author : Allan M. Krall
Publisher : Birkhäuser
Page : 355 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881555

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Hilbert Space, Boundary Value Problems and Orthogonal Polynomials by Allan M. Krall Pdf

The following tract is divided into three parts: Hilbert spaces and their (bounded and unbounded) self-adjoint operators, linear Hamiltonian systemsand their scalar counterparts and their application to orthogonal polynomials. In a sense, this is an updating of E. C. Titchmarsh's classic Eigenfunction Expansions. My interest in these areas began in 1960-61, when, as a graduate student, I was introduced by my advisors E. J. McShane and Marvin Rosenblum to the ideas of Hilbert space. The next year I was given a problem by Marvin Rosenblum that involved a differential operator with an "integral" boundary condition. That same year I attended a class given by the Physics Department in which the lecturer discussed the theory of Schwarz distributions and Titchmarsh's theory of singular Sturm-Liouville boundary value problems. I think a Professor Smith was the in structor, but memory fails. Nonetheless, I am deeply indebted to him, because, as we shall see, these topics are fundamental to what follows. I am also deeply indebted to others. First F. V. Atkinson stands as a giant in the field. W. N. Everitt does likewise. These two were very encouraging to me during my younger (and later) years. They did things "right." It was a revelation to read the book and papers by Professor Atkinson and the many fine fundamen tal papers by Professor Everitt. They are held in highest esteem, and are given profound thanks.

Playing Around Resonance

Alessandro Fonda
Playing Around Resonance Book PDF

Author : Alessandro Fonda
Publisher : Birkhäuser
Page : 309 pages
File Size : 51,8 Mb
Release : 2016-11-11
Category : Mathematics
ISBN : 9783319470900

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Playing Around Resonance by Alessandro Fonda Pdf

This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.

Hilbert Space Methods in Partial Differential Equations

Ralph E. Showalter
Hilbert Space Methods in Partial Differential Equations Book PDF

Author : Ralph E. Showalter
Publisher : Courier Corporation
Page : 226 pages
File Size : 43,8 Mb
Release : 2011-09-12
Category : Mathematics
ISBN : 9780486135793

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Hilbert Space Methods in Partial Differential Equations by Ralph E. Showalter Pdf

This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

Second Order Partial Differential Equations in Hilbert Spaces. London Mathematical Society Lecture Note Series

Giuseppe Da Prato
Second Order Partial Differential Equations in Hilbert Spaces London Mathematical Society Lecture Note Series Book PDF

Author : Giuseppe Da Prato
Publisher : Unknown
Page : 397 pages
File Size : 44,5 Mb
Release : 2002
Category : Electronic
ISBN : 0511177275

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Second Order Partial Differential Equations in Hilbert Spaces. London Mathematical Society Lecture Note Series by Giuseppe Da Prato Pdf

Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is t.

Applied Analysis by the Hilbert Space Method

Samuel S. Holland
Applied Analysis by the Hilbert Space Method Book PDF

Author : Samuel S. Holland
Publisher : Courier Corporation
Page : 578 pages
File Size : 40,9 Mb
Release : 2007-06-05
Category : Mathematics
ISBN : 9780486458014

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Applied Analysis by the Hilbert Space Method by Samuel S. Holland Pdf

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.

M.G. Krein’s Lectures on Entire Operators

Valentina Gorbachuk
M G Krein s Lectures on Entire Operators Book PDF

Author : Valentina Gorbachuk
Publisher : Birkhäuser
Page : 228 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889025

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M.G. Krein’s Lectures on Entire Operators by Valentina Gorbachuk Pdf

This book is devoted to the theory of entire Hermitian operators, an important branch of functional analysis harmoniously combining the methods of operator theory and the theory of analytic functions. This theory anables various problems of classical and modern analysis to be looked at from a uniform point of view. In addition, it serves as a source for setting and solving many new problems in both theories. The three chapters of the book are based on the notes written by his students of M. G. Krein's lectures on the theory of entire operators with (1,1) deficiency index which he delivered in 1961 at the Pedagogical Institute of Odessa, and on his works on the extension theory of Hermitian operators and the theory of analytic functions. The theory is further developed in the direction of solving the problems set up by Krein at ICM-66 in the first two appendices. The first concerns the case of Hermitian operators with arbitrary defect numbers, entire with respect to an ordinary gauge and to a generalized one as well. The other focuses on the entire operators representable by differential operators. The third appendix is the translation from Russian of the unpublished notes of Krein's lecture in which, in particular, the place of the theory of entire operators in the whole analysis is elucidated. In Krein's mathematical heritage the theory of entire operators occupies a special position.

Elliptic Partial Differential Equations of Second Order

David Gilbarg,Neil S. Trudinger
Elliptic Partial Differential Equations of Second Order Book PDF

Author : David Gilbarg,Neil S. Trudinger
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 42,9 Mb
Release : 2001-01-12
Category : Mathematics
ISBN : 3540411607

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Elliptic Partial Differential Equations of Second Order by David Gilbarg,Neil S. Trudinger Pdf

This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.

Series in Banach Spaces

Vladimir Kadets
Series in Banach Spaces Book PDF

Author : Vladimir Kadets
Publisher : Birkhäuser
Page : 162 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034891967

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Series in Banach Spaces by Vladimir Kadets Pdf

Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon ditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements.