Inverse Sturm Liouville Problems And Their Applications

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Inverse Sturm-Liouville Problems and Their Applications

Author : G. Freiling
Publisher : Nova Biomedical Books
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.X/5 (4 download)

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Book Synopsis Inverse Sturm-Liouville Problems and Their Applications by : G. Freiling

Download or read book Inverse Sturm-Liouville Problems and Their Applications written by G. Freiling and published by Nova Biomedical Books. This book was released on 2001 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the main results and methods on inverse spectral problems for Sturm-Liouville differential operators and their applications. Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural sciences. Inverse problems also play an important role in solving non-linear evolution equations in mathematical physics. Interest in this subject has been increasing permanently because of the appearance of new important applications, resulting in intensive study of inverse problem theory all over the world.

Direct and Inverse Sturm-Liouville Problems

Author : Vladislav V. Kravchenko
Publisher : Birkhäuser
ISBN 13 : 9783030478483
Total Pages : 154 pages
Book Rating : 4.4/5 (784 download)

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Book Synopsis Direct and Inverse Sturm-Liouville Problems by : Vladislav V. Kravchenko

Download or read book Direct and Inverse Sturm-Liouville Problems written by Vladislav V. Kravchenko and published by Birkhäuser. This book was released on 2020-08-18 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Inverse Sturm-Liouville Problems

Author : B. M. Levitan
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110941937
Total Pages : 252 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Inverse Sturm-Liouville Problems by : B. M. Levitan

Download or read book Inverse Sturm-Liouville Problems written by B. M. Levitan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-12 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in inverse problems of spectral analysis has increased considerably in recent years due to the applications to important non-linear equations in mathematical physics. This monograph is devoted to the detailed theory of inverse problems and methods of their solution for the Sturm-Liouville case. Chapters 1--6 contain proofs which are, in many cases, very different from those known earlier. Chapters 4--6 are devoted to inverse problems of quantum scattering theory with attention being focused on physical applications. Chapters 7--11 are based on the author's recent research on the theory of finite- and infinite-zone potentials. A chapter discussing the applications to the Korteweg--de Vries problem is also included. This monograph is important reading for all researchers in the field of mathematics and physics.

Sturm-Liouville Operators and Applications

Author : Vladimir Aleksandrovich Marchenko
Publisher : American Mathematical Soc.
ISBN 13 : 0821853163
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Sturm-Liouville Operators and Applications by : Vladimir Aleksandrovich Marchenko

Download or read book Sturm-Liouville Operators and Applications written by Vladimir Aleksandrovich Marchenko and published by American Mathematical Soc.. This book was released on 2011-04-27 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. This book aims to show what can be achieved with the aid of transformation operators in spectral theory as well as their applications.

Sturm-Liouville Theory and its Applications

Author : Mohammed Al-Gwaiz
Publisher : Springer Science & Business Media
ISBN 13 : 1846289718
Total Pages : 270 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Sturm-Liouville Theory and its Applications by : Mohammed Al-Gwaiz

Download or read book Sturm-Liouville Theory and its Applications written by Mohammed Al-Gwaiz and published by Springer Science & Business Media. This book was released on 2008-01-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The text’s presentation follows a clear, rigorous mathematical style that is highly readable. The author first establishes the basic results of Sturm-Liouville theory and then provides examples and applications to illustrate the theory. The final two chapters, on Fourier and Laplace transformations, demonstrate the use of the Fourier series method for representing functions to integral representations.

Sturm-Liouville Theory

Author : Werner O. Amrein
Publisher : Springer Science & Business Media
ISBN 13 : 3764373598
Total Pages : 348 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Sturm-Liouville Theory by : Werner O. Amrein

Download or read book Sturm-Liouville Theory written by Werner O. Amrein and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations

Author : Pham Loi Vu
Publisher : CRC Press
ISBN 13 : 100087205X
Total Pages : 453 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations by : Pham Loi Vu

Download or read book Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations written by Pham Loi Vu and published by CRC Press. This book was released on 2023-05-15 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics. In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students who are approaching them for the first time. New to the Second Edition All new chapter dealing with the Bäcklund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line Updated references and concluding remarks Features Solving the direct and ISP, then solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs are carried out step-by-step. The unknown boundary values are calculated with the help of the Lax (generalized) equations, then the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. Thereby, the potential functions are recovered uniquely in terms of the given initial and calculated boundary conditions. The unique solvability of the ISP is proved and the SD of the scattering problem is described completely. The considered ISPs are well-solved. The ISPs are set up appropriately for constructing the Bӓckhund transformations (BTs) for solutions of associated IBVPs or IVPs for NLEEs. The procedure for finding a BT for the IBVP for NLEEs on the half-line differs from the one used for obtaining a BT for non-linear differential equations defined in the whole space. The interrelations between the ISPs and the constructed BTs are established to become new powerful unified transformations (UTs) for solving IBVPs or IVPs for NLEEs, that can be used in different areas of physics and mechanics. The application of the UTs is consistent and efficiently embedded in the scheme of the associated ISP.

Inverse problems in vibration

Author : G.M.L. Gladwell
Publisher : Springer Science & Business Media
ISBN 13 : 9401511780
Total Pages : 272 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Inverse problems in vibration by : G.M.L. Gladwell

Download or read book Inverse problems in vibration written by G.M.L. Gladwell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last thing one settles in writing a book is what one should put in first. Pascal's Pensees Classical vibration theory is concerned, in large part, with the infinitesimal (i. e. , linear) undamped free vibration of various discrete or continuous bodies. One of the basic problems in this theory is the determination of the natural frequencies (eigen frequencies or simply eigenvalues) and normal modes of the vibrating body. A body which is modelled as a discrete system' of rigid masses, rigid rods, massless springs, etc. , will be governed by an ordinary matrix differential equation in time t. It will have a finite number of eigenvalues, and the normal modes will be vectors, called eigenvectors. A body which is modelled as a continuous system will be governed by a partial differential equation in time and one or more spatial variables. It will have an infinite number of eigenvalues, and the normal modes will be functions (eigen functions) of the space variables. In the context of this classical theory, inverse problems are concerned with the construction of a model of a given type; e. g. , a mass-spring system, a string, etc. , which has given eigenvalues and/or eigenvectors or eigenfunctions; i. e. , given spec tral data. In general, if some such spectral data is given, there can be no system, a unique system, or many systems, having these properties.

Spectral Theory & Computational Methods of Sturm-Liouville Problems

Author : Don Hinton
Publisher : CRC Press
ISBN 13 : 9780824700300
Total Pages : 422 pages
Book Rating : 4.7/5 (3 download)

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Book Synopsis Spectral Theory & Computational Methods of Sturm-Liouville Problems by : Don Hinton

Download or read book Spectral Theory & Computational Methods of Sturm-Liouville Problems written by Don Hinton and published by CRC Press. This book was released on 1997-05-06 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the proceedings of the conference on Sturm-Liouville problems held in conjunction with the 26th Barrett Memorial Lecture Series at the University of Tennessee, Knoxville, this text covers both qualitative and computational theory of Sturm-Liouville problems. It surveys questions in the field as well as describing applications and concepts.

Direct and Inverse Sturm-Liouville Problems

Author : Vladislav V. Kravchenko
Publisher : Springer Nature
ISBN 13 : 3030478491
Total Pages : 155 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Direct and Inverse Sturm-Liouville Problems by : Vladislav V. Kravchenko

Download or read book Direct and Inverse Sturm-Liouville Problems written by Vladislav V. Kravchenko and published by Springer Nature. This book was released on 2020-07-28 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Inverse Spectral Problems for Linear Differential Operators and Their Applications

Author : V A Yurko
Publisher : CRC Press
ISBN 13 : 1482287439
Total Pages : 272 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Inverse Spectral Problems for Linear Differential Operators and Their Applications by : V A Yurko

Download or read book Inverse Spectral Problems for Linear Differential Operators and Their Applications written by V A Yurko and published by CRC Press. This book was released on 2000-01-18 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spe

An Introduction to Inverse Scattering and Inverse Spectral Problems

Author : Khosrow Chadan
Publisher : SIAM
ISBN 13 : 0898713870
Total Pages : 206 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis An Introduction to Inverse Scattering and Inverse Spectral Problems by : Khosrow Chadan

Download or read book An Introduction to Inverse Scattering and Inverse Spectral Problems written by Khosrow Chadan and published by SIAM. This book was released on 1997-01-01 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.

Inverse Spectral Theory

Author : Jurgen Poschel
Publisher : Academic Press
ISBN 13 : 0080874495
Total Pages : 209 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Inverse Spectral Theory by : Jurgen Poschel

Download or read book Inverse Spectral Theory written by Jurgen Poschel and published by Academic Press. This book was released on 1987-03-16 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Spectral Theory

Inverse Eigenvalue Problems

Author : Moody Chu
Publisher : Oxford University Press
ISBN 13 : 0198566646
Total Pages : 408 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Inverse Eigenvalue Problems by : Moody Chu

Download or read book Inverse Eigenvalue Problems written by Moody Chu and published by Oxford University Press. This book was released on 2005-06-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.

Introduction to Quantum Graphs

Author : Gregory Berkolaiko
Publisher : American Mathematical Soc.
ISBN 13 : 0821892118
Total Pages : 291 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Quantum Graphs by : Gregory Berkolaiko

Download or read book Introduction to Quantum Graphs written by Gregory Berkolaiko and published by American Mathematical Soc.. This book was released on 2013 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

Dynamical Inverse Problems: Theory and Application

Author : Graham M. L. Gladwell
Publisher : Springer Science & Business Media
ISBN 13 : 3709106966
Total Pages : 229 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Dynamical Inverse Problems: Theory and Application by : Graham M. L. Gladwell

Download or read book Dynamical Inverse Problems: Theory and Application written by Graham M. L. Gladwell and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.

Sturm-Liouville Theory

Author : Werner O. Amrein
Publisher : Birkhäuser
ISBN 13 : 9783764390228
Total Pages : 336 pages
Book Rating : 4.3/5 (92 download)

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Book Synopsis Sturm-Liouville Theory by : Werner O. Amrein

Download or read book Sturm-Liouville Theory written by Werner O. Amrein and published by Birkhäuser. This book was released on 2009-09-03 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.