Download or read book Completeness of Root Functions of Regular Differential Operators written by Sasun Yakubov and published by CRC Press. This book was released on 1993-12-20 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The precise mathematical investigation of various natural phenomena is an old and difficult problem. This book is the first to deal systematically with the general non-selfadjoint problems in mechanics and physics. It deals mainly with bounded domains with smooth boundaries, but also considers elliptic boundary value problems in tube domains, i.e. in non-smooth domains. This volume will be of particular value to those working in differential equations, functional analysis, and equations of mathematical physics.

Download or read book Completeness of Root Functions of Regular Differential Operators written by Sasun Yakubov and published by Routledge. This book was released on 2021-12-17 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The precise mathematical investigation of various natural phenomena is an old and difficult problem. This book is the first to deal systematically with the general non-selfadjoint problems in mechanics and physics. It deals mainly with bounded domains with smooth boundaries, but also considers elliptic boundary value problems in tube domains, i.e. in non-smooth domains. This volume will be of particular value to those working in differential equations, functional analysis, and equations of mathematical physics.

Download or read book Differential Operator Equations written by Yakov Yakubov and published by CRC Press. This book was released on 1999-11-24 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of differential-operator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics. Although a number of published works address differential-operator equations of the first and second orders, to date none offer a treatment of the higher orders. In Differential-Operator Equations, the authors present a systematic treatment of the theory of differential-operator equations of higher order, with applications to partial differential equations. They construct a theory that allows application to both regular and irregular differential problems. In particular, they study problems that cannot be solved by various known methods and irregular problems not addressed in existing monographs. These include Birkhoff-irregularity, non-local boundary value conditions, and non-smoothness of the boundary of the domains. Among this volume's other points of interest are: The Abel basis property of a system of root functions Irregular boundary value problems The theory of hyperbolic equations in Gevrey space The theory of boundary value problems for elliptic differential equations with a parameter

Download or read book Eigenvalues and Completeness for Regular and Simply Irregular Two Point Differential Operators written by John Locker and published by American Mathematical Soc.. This book was released on 2008 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the author develops the spectral theory for an $n$th order two-point differential operator $L$ in the Hilbert space $L2[0,1]$, where $L$ is determined by an $n$th order formal differential operator $\ell$ having variable coefficients and by $n$ linearly independent boundary values $B 1, \ldots, B n$. Using the Birkhoff approximate solutions of the differential equation $(\rhon I - \ell)u = 0$, the differential operator $L$ is classified as belonging to one of threepossible classes: regular, simply irregular, or degenerate irregular. For the regular and simply irregular classes, the author develops asymptotic expansions of solutions of the differential equation $(\rhon I - \ell)u = 0$, constructs the characteristic determinant and Green's function,characterizes the eigenvalues and the corresponding algebraic multiplicities and ascents, and shows that the generalized eigenfunctions of $L$ are complete in $L2[0,1]$. He also gives examples of degenerate irregular differential operators illustrating some of the unusual features of this class.

Download or read book Spectral Theory of Non Self Adjoint Two Point Differential Operators written by John Locker and published by American Mathematical Soc.. This book was released on 2000 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the spectral theory of an nth order non-self-adjoint two- point differential operator L in the complex Hilbert space L2[0,1]. The differential operator L is determined by an nth order formal differential l and by n linearly independent boundary values B1,.,Bn. Locker first lays the foundations of the spectral theory for closed linear operators and Fredholm operators in Hilbert spaces before developing the spectral theory of the differential operator L. The book is a sequel to Functional analysis and two-point differential operators, 1986. Annotation copyrighted by Book News, Inc., Portland, OR.

Download or read book Application of Abstract Differential Equations to Some Mechanical Problems written by I. Titeux and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: PREFACE The theory of differential-operator equations has been described in various monographs, but the initial physical problem which leads to these equations is often hidden. When the physical problem is studied, the mathematical proofs are either not given or are quickly explained. In this book, we give a systematic treatment of the partial differential equations which arise in elastostatic problems. In particular, we study problems which are obtained from asymptotic expansion with two scales. Here the methods of operator pencils and differential-operator equations are used. This book is intended for scientists and graduate students in Functional Analy sis, Differential Equations, Equations of Mathematical Physics, and related topics. It would undoubtedly be very useful for mechanics and theoretical physicists. We would like to thank Professors S. Yakubov and S. Kamin for helpfull dis cussions of some parts of the book. The work on the book was also partially supported by the European Community Program RTN-HPRN-CT-2002-00274. xiii INTRODUCTION In first two sections of the introduction, a classical mathematical problem will be exposed: the Laplace problem. The domain of definition will be, on the first time, an infinite strip and on the second time, a sector. To solve this problem, a well known separation of variables method will be used. In this way, the structure of the solution can be explicitly found. For more details about the separation of variables method exposed in this part, the reader can refer to, for example, the book by D. Leguillon and E. Sanchez-Palencia [LS].

Download or read book Partial Differential Equations IX written by M.S. Agranovich and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.

Download or read book Recent Developments in Operator Theory and Its Applications written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers selected for publication here, many of them written by leaders in the field, bring readers up to date on recent achievements in modern operator theory and applications. The book’s subject matter is of practical use to a wide audience in mathematical and engineering sciences.

Download or read book Introduction to the Spectral Theory of Polynomial Operator Pencils written by A. S. Markus and published by American Mathematical Soc.. This book was released on 2012-09-14 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Krein and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, researchers in mechanics, and theoretical physicists interested in spectral theory and its applications, the book assumes a familiarity with the fundamentals of spectral theory of operators acting in a Hilbert space.

Download or read book Issues in Calculus Mathematical Analysis and Nonlinear Research 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Mathematical Analysis. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematical Analysis in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book Partial Differential Equations VI written by Yu.V. Egorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject.

Download or read book Linear Differential Operators written by Cornelius Lanczos and published by Courier Corporation. This book was released on 1997-01-01 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic and characteristic properties of linear differential operators are explored in this graduate-level text. No specific knowledge beyond the usual introductory courses is necessary. Includes 350 problems and solution.

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Download or read book Differential and Integral Equations written by and published by . This book was released on 1997 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Denseness Bases and Frames in Banach Spaces and Applications written by Aref Jeribi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

Download or read book Proceedings of the Tunisian Mathematical Society Volume 11 written by K. Trimeche and published by Nova Publishers. This book was released on 2006 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings consist of ten carefully refereed and selected papers which were presented at the 12th symposium of Tunisian Mathematical Society held on March 18-23, 2004 in Mahdia (Tunisia). This symposium was one of the largest international meeting on Mathematics in Tunisia. A total of 200 participants from several countries attended to the meeting. In addition to the plenary, invited and contributed talks, there was a panel discussion on future research directions and problems in various areas of mathematics.

Download or read book Spectral Geometry of Partial Differential Operators written by Michael Ruzhansky and published by CRC Press. This book was released on 2020-02-07 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations. Historically, one of the first inequalities of the spectral geometry was the minimization problem of the first eigenvalue of the Dirichlet Laplacian. Nowadays, this type of inequalities of spectral geometry have expanded to many other cases with number of applications in physics and other sciences. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of (partial differential) operators on arbitrary domains. Features: Collects the ideas underpinning the inequalities of the spectral geometry, in both self-adjoint and non-self-adjoint operator theory, in a way accessible by anyone with a basic level of understanding of linear differential operators Aimed at theoretical as well as applied mathematicians, from a wide range of scientific fields, including acoustics, astronomy, MEMS, and other physical sciences Provides a step-by-step guide to the techniques of non-self-adjoint partial differential operators, and for the applications of such methods. Provides a self-contained coverage of the traditional and modern theories of linear partial differential operators, and does not require a previous background in operator theory.