Boundary Value Problems, Weyl Functions, and Differential Operators

Boundary Value Problems, Weyl Functions, and Differential Operators PDF

Author: Jussi Behrndt

Publisher: Springer Nature

Published: 2020-01-03

Total Pages: 772

ISBN-13: 3030367142

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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.

Understanding Boundary Value Problems, Weyl Functions and Differential Operators: Volume 3

Understanding Boundary Value Problems, Weyl Functions and Differential Operators: Volume 3 PDF

Author: Williams Gerald

Publisher: Murphy & Moore Publishing

Published: 2021-11-16

Total Pages: 275

ISBN-13: 9781639875498

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Boundary value problems are differential equations with a set of additional constraints, called the boundary conditions. A solution which satisfies the boundary conditions is a solution to the boundary value problem and the differential equation. The Weyl distance function behaves in some ways like the distance function of a metric space. It takes values in a group of reflections, instead of taking values in the positive real numbers. This group of reflections is called the Weyl group. A differential operator is a function of the differentiation operator, also known as the derivative. Differentiation can be considered as an abstract operation that accepts a function and returns another function. This book provides significant information of this discipline to help develop a good understanding of boundary value problems, Weyl functions, differential operators and related fields. It presents this complex subject in the most comprehensible and easy to understand language. Constant effort has been made in this book, using case studies and examples, to make the understanding of these difficult concepts of mathematics as easy and informative as possible to the readers.

Understanding Boundary Value Problems, Weyl Functions and Differential Operators: Volume 1

Understanding Boundary Value Problems, Weyl Functions and Differential Operators: Volume 1 PDF

Author: Williams Gerald

Publisher: Murphy & Moore Publishing

Published: 2021-11-16

Total Pages: 233

ISBN-13: 9781639875474

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Boundary value problems are differential equations with a set of additional constraints, called the boundary conditions. A solution which satisfies the boundary conditions is a solution to the boundary value problem and the differential equation. The Weyl distance function behaves in some ways like the distance function of a metric space. It takes values in a group of reflections, instead of taking values in the positive real numbers. This group of reflections is called the Weyl group. A differential operator is a function of the differentiation operator, also known as the derivative. Differentiation can be considered as an abstract operation that accepts a function and returns another function. This book provides significant information of this discipline to help develop a good understanding of boundary value problems, Weyl functions, differential operators and related fields. It presents this complex subject in the most comprehensible and easy to understand language. Constant effort has been made in this book, using case studies and examples, to make the understanding of these difficult concepts of mathematics as easy and informative as possible to the readers.

Understanding Boundary Value Problems, Weyl Functions and Differential Operators: Volume 2

Understanding Boundary Value Problems, Weyl Functions and Differential Operators: Volume 2 PDF

Author: Williams Gerald

Publisher: Murphy & Moore Publishing

Published: 2021-11-16

Total Pages: 286

ISBN-13: 9781639875481

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Boundary value problems are differential equations with a set of additional constraints, called the boundary conditions. A solution which satisfies the boundary conditions is a solution to the boundary value problem and the differential equation. The Weyl distance function behaves in some ways like the distance function of a metric space. It takes values in a group of reflections, instead of taking values in the positive real numbers. This group of reflections is called the Weyl group. A differential operator is a function of the differentiation operator, also known as the derivative. Differentiation can be considered as an abstract operation that accepts a function and returns another function. This book provides significant information of this discipline to help develop a good understanding of boundary value problems, Weyl functions, differential operators and related fields. It presents this complex subject in the most comprehensible and easy to understand language. Constant effort has been made in this book, using case studies and examples, to make the understanding of these difficult concepts of mathematics as easy and informative as possible to the readers.

Operator Methods for Boundary Value Problems

Operator Methods for Boundary Value Problems PDF

Author: Seppo Hassi

Publisher: Cambridge University Press

Published: 2012-10-11

Total Pages: 297

ISBN-13: 1139561316

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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.

Boundary Value Problems for Elliptic Systems

Boundary Value Problems for Elliptic Systems PDF

Author: J. T. Wloka

Publisher: Cambridge University Press

Published: 1995-07-28

Total Pages: 659

ISBN-13: 0521430119

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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.

Elliptic Boundary Value Problems in Domains with Point Singularities

Elliptic Boundary Value Problems in Domains with Point Singularities PDF

Author: Vladimir Kozlov

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 426

ISBN-13: 0821807544

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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

From Complex Analysis to Operator Theory: A Panorama

From Complex Analysis to Operator Theory: A Panorama PDF

Author: Malcolm Brown

Publisher: Springer Nature

Published: 2023-09-21

Total Pages: 731

ISBN-13: 3031311396

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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.

Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems

Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems PDF

Author: Graef John R

Publisher: World Scientific

Published: 2018-09-18

Total Pages: 344

ISBN-13: 9813274042

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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.

Operators, Semigroups, Algebras and Function Theory

Operators, Semigroups, Algebras and Function Theory PDF

Author: Yemon Choi

Publisher: Springer Nature

Published: 2023-12-06

Total Pages: 262

ISBN-13: 3031380207

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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.

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