Boundary Value Problems Weyl Functions And Differential Operators

Author : Jussi Behrndt,Seppo Hassi,Henk de Snoo
Publisher : Springer Nature
Page : 772 pages
File Size : 52,5 Mb
Release : 2020-01-03
Category : Mathematics
ISBN : 9783030367145

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Boundary Value Problems, Weyl Functions, and Differential Operators by Jussi Behrndt,Seppo Hassi,Henk de Snoo Pdf

This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

Author : Seppo Hassi,Hendrik S. V. de Snoo,Franciszek Hugon Szafraniec
Publisher : Cambridge University Press
Page : 297 pages
File Size : 44,6 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9781139561310

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Operator Methods for Boundary Value Problems by Seppo Hassi,Hendrik S. V. de Snoo,Franciszek Hugon Szafraniec Pdf

Presented in this volume are a number of new results concerning the extension theory and spectral theory of unbounded operators using the recent notions of boundary triplets and boundary relations. This approach relies on linear single-valued and multi-valued maps, isometric in a Krein space sense, and offers a basic framework for recent developments in system theory. Central to the theory are analytic tools such as Weyl functions, including Titchmarsh-Weyl m-functions and Dirichlet-to-Neumann maps. A wide range of topics is considered in this context from the abstract to the applied, including boundary value problems for ordinary and partial differential equations; infinite-dimensional perturbations; local point-interactions; boundary and passive control state/signal systems; extension theory of accretive, sectorial and symmetric operators; and Calkin's abstract boundary conditions. This accessible treatment of recent developments, written by leading researchers, will appeal to a broad range of researchers, students and professionals.

Author : Xiaochun Liu,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 410 pages
File Size : 50,5 Mb
Release : 2018-10-30
Category : Mathematics
ISBN : 9783319701141

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Boundary Value Problems with Global Projection Conditions by Xiaochun Liu,Bert-Wolfgang Schulze Pdf

This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. In this regard, every operator admits global projection boundary conditions, giving rise to analogues of Toeplitz operators in subspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel’s calculus, as well as for operators on manifolds with edges, including the case of operators without the transmission property. Further, it shows how the calculus contains parametrices of elliptic elements. Lastly, the book describes natural connections to ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and the characterization of Cauchy data spaces.

Author : Myroslav L. Gorbachuk
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401137140

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Boundary Value Problems for Operator Differential Equations by Myroslav L. Gorbachuk Pdf

Author : J. T. Wloka,B. Rowley,B. Lawruk
Publisher : Cambridge University Press
Page : 659 pages
File Size : 40,7 Mb
Release : 1995-07-28
Category : Mathematics
ISBN : 9780521430111

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Boundary Value Problems for Elliptic Systems by J. T. Wloka,B. Rowley,B. Lawruk Pdf

The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. Because many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises. This book is ideal for use in graduate level courses on partial differential equations, elliptic systems, pseudo-differential operators, and matrix analysis.

Author : Malcolm Brown,Fritz Gesztesy,Pavel Kurasov,Ari Laptev,Barry Simon,Gunter Stolz,Ian Wood
Publisher : Springer Nature
Page : 731 pages
File Size : 49,9 Mb
Release : 2023-09-21
Category : Mathematics
ISBN : 9783031311390

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From Complex Analysis to Operator Theory: A Panorama by Malcolm Brown,Fritz Gesztesy,Pavel Kurasov,Ari Laptev,Barry Simon,Gunter Stolz,Ian Wood Pdf

This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Author : Ivar Stakgold
Publisher : SIAM
Page : 1156 pages
File Size : 51,6 Mb
Release : 2000-06-30
Category : Science
ISBN : 9780898714562

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Boundary Value Problems of Mathematical Physics by Ivar Stakgold Pdf

For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problems using Green's functions and using eigenvalue expansions. Now a part of SIAM's Classics series, these volumes contain a large number of concrete, interesting examples of boundary value problems for partial differential equations that cover a variety of applications that are still relevant today. For example, there is substantial treatment of the Helmholtz equation and scattering theory?subjects that play a central role in contemporary inverse problems in acoustics and electromagnetic theory.

Author : V. A. Kozlov,V. G. Mazʹi︠a︡,J. Rossmann,Jürgen Rossmann
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 54,9 Mb
Release : 1997
Category : Boundary value problems
ISBN : 9780821807545

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Elliptic Boundary Value Problems in Domains with Point Singularities by V. A. Kozlov,V. G. Mazʹi︠a︡,J. Rossmann,Jürgen Rossmann Pdf

For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Bashir Ahmad,Johnny L Henderson,Rodica Luca
Publisher : World Scientific
Page : 468 pages
File Size : 45,6 Mb
Release : 2021-02-18
Category : Mathematics
ISBN : 9789811224478

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Boundary Value Problems For Fractional Differential Equations And Systems by Bashir Ahmad,Johnny L Henderson,Rodica Luca Pdf

This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.

Author : Graef John R,Henderson Johnny L,Kong Lingju
Publisher : World Scientific
Page : 344 pages
File Size : 55,7 Mb
Release : 2018-09-18
Category : Mathematics
ISBN : 9789813274044

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Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems by Graef John R,Henderson Johnny L,Kong Lingju Pdf

The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.

Author : Yemon Choi,Matthew Daws,Gordon Blower
Publisher : Springer Nature
Page : 262 pages
File Size : 51,7 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 9783031380204

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Operators, Semigroups, Algebras and Function Theory by Yemon Choi,Matthew Daws,Gordon Blower Pdf

This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.

Author : William Norrie Everitt,Lawrence Markus
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 54,8 Mb
Release : 1999
Category : Boundary value problems
ISBN : 9780821810804

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Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators by William Norrie Everitt,Lawrence Markus Pdf

In the classical theory of self-adjoint boundary value problems for linear ordinary differential operators there is a fundamental, but rather mysterious, interplay between the symmetric (conjugate) bilinear scalar product of the basic Hilbert space and the skew-symmetric boundary form of the associated differential expression. This book presents a new conceptual framework, leading to an effective structured method, for analysing and classifying all such self-adjoint boundary conditions. The program is carried out by introducing innovative new mathematical structures which relate the Hilbert space to a complex symplectic space. This work offers the first systematic detailed treatment in the literature of these two topics: complex symplectic spaces--their geometry and linear algebra--and quasi-differential operators.

Author : Leon Cohen
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 47,9 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034802949

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The Weyl Operator and its Generalization by Leon Cohen Pdf

The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar. This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner.

Author : Ravi P Agarwal
Publisher : World Scientific
Page : 321 pages
File Size : 42,9 Mb
Release : 1986-07-01
Category : Mathematics
ISBN : 9789814513630

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Boundary Value Problems From Higher Order Differential Equations by Ravi P Agarwal Pdf

Contents: Some ExamplesLinear ProblemsGreen's FunctionMethod of Complementary FunctionsMethod of AdjointsMethod of ChasingSecond Order EquationsError Estimates in Polynomial InterpolationExistence and UniquenessPicard's and Approximate Picard's MethodQuasilinearization and Approximate QuasilinearizationBest Possible Results: Weight Function TechniqueBest Possible Results: Shooting MethodsMonotone Convergence and Further ExistenceUniqueness Implies ExistenceCompactness Condition and Generalized SolutionsUniqueness Implies UniquenessBoundary Value FunctionsTopological MethodsBest Possible Results: Control Theory MethodsMatching MethodsMaximal SolutionsMaximum PrincipleInfinite Interval ProblemsEquations with Deviating Arguments Readership: Graduate students, numerical analysts as well as researchers who are studying open problems. Keywords:Boundary Value Problems;Ordinary Differential Equations;Green's Function;Quasilinearization;Shooting Methods;Maximal Solutions;Infinite Interval Problems

Author : Alexander Andreevych Boichuk,Anatolii M. Samoilenko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 314 pages
File Size : 54,5 Mb
Release : 2016-08-22
Category : Mathematics
ISBN : 9783110387353

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Generalized Inverse Operators by Alexander Andreevych Boichuk,Anatolii M. Samoilenko Pdf

The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form. A common point of view on numerous classes of problems that were traditionally studied independently of each other enables us to study, in a natural way, the theory of these problems, to supplement and improve the existing results, and in certain cases, study some of these problems for the first time. With the help of the technique of generalized inverse operators, the Vishik– Lyusternik method, and iterative methods, we perform a detailed investigation of the problems of existence, bifurcations, and branching of the solutions of linear and nonlinear boundary-value problems for various classes of differential-operator systems and propose new procedures for their construction. For more than 11 years that have passed since the appearance of the first edition of the monograph, numerous new publications of the authors in this direction have appeared. In this connection, it became necessary to make some additions and corrections to the previous extensively cited edition, which is still of signifi cant interest for the researchers. For researchers, teachers, post-graduate students, and students of physical and mathematical departments of universities. Contents: Preliminary Information Generalized Inverse Operators in Banach Spaces Pseudoinverse Operators in Hilbert Spaces Boundary-Value Problems for Operator Equations Boundary-Value Problems for Systems of Ordinary Differential Equations Impulsive Boundary-Value Problems for Systems of Ordinary Differential Equations Solutions of Differential and Difference Systems Bounded on the Entire Real Axis