Direct And Inverse Sturm Liouville Problems

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Direct and Inverse Sturm-Liouville Problems

Vladislav V. Kravchenko
Direct and Inverse Sturm Liouville Problems Book PDF

Author : Vladislav V. Kravchenko
Publisher : Springer Nature
Page : 155 pages
File Size : 44,5 Mb
Release : 2020-07-28
Category : Mathematics
ISBN : 9783030478490

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Direct and Inverse Sturm-Liouville Problems by Vladislav V. Kravchenko Pdf

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

B. M. Levitan
Inverse Sturm Liouville Problems Book PDF

Author : B. M. Levitan
Publisher : Walter de Gruyter GmbH & Co KG
Page : 252 pages
File Size : 43,5 Mb
Release : 2018-07-12
Category : Mathematics
ISBN : 9783110941937

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Inverse Sturm-Liouville Problems by B. M. Levitan Pdf

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.

Direct and Inverse Finite-Dimensional Spectral Problems on Graphs

Manfred Möller,Vyacheslav Pivovarchik
Direct and Inverse Finite Dimensional Spectral Problems on Graphs Book PDF

Author : Manfred Möller,Vyacheslav Pivovarchik
Publisher : Springer Nature
Page : 349 pages
File Size : 49,9 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030604844

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Direct and Inverse Finite-Dimensional Spectral Problems on Graphs by Manfred Möller,Vyacheslav Pivovarchik Pdf

Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of finding strings with a prescribed spectrum are considered. This monograph gives a comprehensive and self-contained account on the subject, thereby also generalizing known results. The interplay between the representation of rational functions and their zeros and poles is at the center of the methods used. The book also unravels connections between finite dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint and non-self-adjoint finite-dimensional problems. This book is addressed to researchers in spectral theory of differential and difference equations as well as physicists and engineers who may apply the presented results and methods to their research.

Sturm-Liouville Theory

Werner O. Amrein,Andreas M. Hinz,David B. Pearson
Sturm Liouville Theory Book PDF

Author : Werner O. Amrein,Andreas M. Hinz,David B. Pearson
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 48,8 Mb
Release : 2005-12-05
Category : Mathematics
ISBN : 9783764373597

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Sturm-Liouville Theory by Werner O. Amrein,Andreas M. Hinz,David B. Pearson Pdf

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.

Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations

Alexander G. Megrabov
Forward and Inverse Problems for Hyperbolic Elliptic and Mixed Type Equations Book PDF

Author : Alexander G. Megrabov
Publisher : Walter de Gruyter
Page : 244 pages
File Size : 41,6 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9783110944983

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Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations by Alexander G. Megrabov Pdf

Inverse problems are an important and rapidly developing direction in mathematics, mathematical physics, differential equations, and various applied technologies (geophysics, optic, tomography, remote sensing, radar-location, etc.). In this monograph direct and inverse problems for partial differential equations are considered. The type of equations focused are hyperbolic, elliptic, and mixed (elliptic-hyperbolic). The direct problems arise as generalizations of problems of scattering plane elastic or acoustic waves from inhomogeneous layer (or from half-space). The inverse problems are those of determination of medium parameters by giving the forms of incident and reflected waves or the vibrations of certain points of the medium. The method of research of all inverse problems is spectral-analytical, consisting in reducing the considered inverse problems to the known inverse problems for the Sturm-Liouville equation or the string equation. Besides the book considers discrete inverse problems. In these problems an arbitrary set of point sources (emissive sources, oscillators, point masses) is determined.

Sturm-Liouville Theory

Werner O. Amrein,Andreas M. Hinz,David B. Pearson
Sturm Liouville Theory Book PDF

Author : Werner O. Amrein,Andreas M. Hinz,David B. Pearson
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 49,7 Mb
Release : 2005-05-19
Category : Mathematics
ISBN : 3764370661

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Sturm-Liouville Theory by Werner O. Amrein,Andreas M. Hinz,David B. Pearson Pdf

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.

Operator Theory and Harmonic Analysis

Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Operator Theory and Harmonic Analysis Book PDF

Author : Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Publisher : Springer Nature
Page : 585 pages
File Size : 45,6 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030774936

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Operator Theory and Harmonic Analysis by Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek Pdf

This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.

Inverse Problems for Fractional Partial Differential Equations

Barbara Kaltenbacher,William Rundell
Inverse Problems for Fractional Partial Differential Equations Book PDF

Author : Barbara Kaltenbacher,William Rundell
Publisher : American Mathematical Society
Page : 522 pages
File Size : 42,7 Mb
Release : 2023-07-17
Category : Mathematics
ISBN : 9781470472450

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Inverse Problems for Fractional Partial Differential Equations by Barbara Kaltenbacher,William Rundell Pdf

As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a PDE, including all coefficients and initial/boundary conditions, and to determine the solution. The inverse problem reverses this approach asking what information about coefficients of the model can be obtained from partial information on the solution. Answering this question requires knowledge of the underlying physical model, including the exact dependence on material parameters. The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case. The book also has an extensive historical section and the material that can be called "fractional calculus" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.

Methods of Mathematical Physics

Alexey N. Karapetyants,Vladislav V. Kravchenko
Methods of Mathematical Physics Book PDF

Author : Alexey N. Karapetyants,Vladislav V. Kravchenko
Publisher : Springer Nature
Page : 406 pages
File Size : 54,9 Mb
Release : 2022-11-17
Category : Science
ISBN : 9783031178450

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Methods of Mathematical Physics by Alexey N. Karapetyants,Vladislav V. Kravchenko Pdf

This textbook provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments. Readers will be introduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in textbooks, this will be an ideal text for both introductory and more specialized courses. The first five chapters present standard material, including the classification of PDEs, an introduction to boundary value and initial value problems, and an introduction to the Fourier method of separation of variables. More advanced material and specialized treatments follow, including practical methods for solving direct and inverse Sturm-Liouville problems; the theory of parabolic equations, harmonic functions, potential theory, integral equations and the method of non-orthogonal series. Methods of Mathematical Physics is ideal for undergraduate students and can serve as a textbook for a regular course in equations of mathematical physics as well as for more advanced courses on selected topics.

Inverse Sturm-Liouville Problems and Their Applications

G. Freiling,V. A. Yurko
Inverse Sturm Liouville Problems and Their Applications Book PDF

Author : G. Freiling,V. A. Yurko
Publisher : Nova Biomedical Books
Page : 324 pages
File Size : 44,6 Mb
Release : 2001
Category : Mathematics
ISBN : UVA:X004635761

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Inverse Sturm-Liouville Problems and Their Applications by G. Freiling,V. A. Yurko Pdf

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.

Sturm-Liouville Theory and its Applications

Mohammed Al-Gwaiz
Sturm Liouville Theory and its Applications Book PDF

Author : Mohammed Al-Gwaiz
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 45,6 Mb
Release : 2008-01-15
Category : Mathematics
ISBN : 9781846289712

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Sturm-Liouville Theory and its Applications by Mohammed Al-Gwaiz Pdf

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.

Sampling Theory in Fourier and Signal Analysis

John Rowland Higgins
Sampling Theory in Fourier and Signal Analysis Book PDF

Author : John Rowland Higgins
Publisher : Unknown
Page : 240 pages
File Size : 50,7 Mb
Release : 1996
Category : Mathematics
ISBN : 0198596995

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Sampling Theory in Fourier and Signal Analysis by John Rowland Higgins Pdf

With much material not previously found in book form, this book fills a gap by discussing the equivalence of signal functions with their sets of values taken at discreet points comprehensively and on a firm mathematical ground. The wide variety of topics begins with an introduction to the main ideas and background material on Fourier analysis and Hilbert spaces and their bases. Other chapters discuss sampling of Bernstein and Paley-Wiener spaces; Kramer's Lemma and its application to eigenvalue problems; contour integral methods including a proof of the equivalence of the sampling theory; the Poisson summation formula and Cauchy's integral formula; optimal regular, irregular, multi-channel, multi-band and multi-dimensional sampling; and Campbell's generalized sampling theorem. Mathematicians, physicists, and communications engineers will welcome the scope of information found here.

Control And Inverse Problems For Partial Differential Equations

Bao Gang,Coron Jean-michel,Li Ta-tsien
Control And Inverse Problems For Partial Differential Equations Book PDF

Author : Bao Gang,Coron Jean-michel,Li Ta-tsien
Publisher : World Scientific
Page : 264 pages
File Size : 44,7 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9789813276161

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Control And Inverse Problems For Partial Differential Equations by Bao Gang,Coron Jean-michel,Li Ta-tsien Pdf

This book is a collection of lecture notes for the LIASFMA Hangzhou Autumn School on 'Control and Inverse Problems for Partial Differential Equations' which was held during October 17-22, 2016 at Zhejiang University, Hangzhou, China. This autumn school is one of the activities organized by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA). Established jointly by eight institutions in China and France in 2014, LIASFMA aims at providing a platform for many leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in broad areas of applied mathematics.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in control and inverse problems. And the readers are exposed not only to the basic theories and methods but also to the forefront of research directions in both fields.

Sturm-Liouville Theory

Anton Zettl
Sturm Liouville Theory Book PDF

Author : Anton Zettl
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 49,5 Mb
Release : 2005
Category : Education
ISBN : 9780821852675

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Sturm-Liouville Theory by Anton Zettl Pdf

In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed. An extensive list of references and examples is provided and numerous open problems are given. The list of examples includes those classical equations and functions associated with the names of Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, Morse, as well as examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.

Method of Spectral Mappings in the Inverse Problem Theory

Vacheslav A. Yurko
Method of Spectral Mappings in the Inverse Problem Theory Book PDF

Author : Vacheslav A. Yurko
Publisher : Walter de Gruyter
Page : 316 pages
File Size : 46,6 Mb
Release : 2013-10-10
Category : Mathematics
ISBN : 9783110940961

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Method of Spectral Mappings in the Inverse Problem Theory by Vacheslav A. Yurko Pdf

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 science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.