Download or read book Bounds for the Eigenvalues of Non selfadjoint Differential Operators written by J. D. P. Donnelly and published by . This book was released on 1972 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalization of the Gerschgorin circle theorem is applied to an infinite matrix representation of a differential operator to obtain bounds for its eigenvalues. (Author).
Download or read book Non Self Adjoint Boundary Eigenvalue Problems written by R. Mennicken and published by Gulf Professional Publishing. This book was released on 2003-06-26 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 'North-Holland Mathematics Studies' series comprises a set of cutting-edge monographs and studies. This volume explores non-self-adjoint boundary eigenvalue problems for first order systems of ordinary differential equations and n-th order scalar differential equations.
Download or read book Guaranteed Computational Methods for Self Adjoint Differential Eigenvalue Problems written by Xuefeng Liu and published by Springer Nature. This book was released on with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Method for Approximating the Eigenvalues of Non Self adjoint Ordinary Differential Operators written by John E. Osborn and published by . This book was released on 1979 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non Self Adjoint Differential Operators Spectral Asymptotics and Random Perturbations written by Johannes Sjöstrand and published by Springer. This book was released on 2019-05-17 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Download or read book Lower Bounds for Higher Eigenvalues of Second Order Operators by Finite Difference Methods written by H. F. WEINBERGER and published by . This book was released on 1957 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lower bounds for all the eigenvalues or an arbitrary second order self-adjoint elliptic differential operator on a bounded domain R with zero boundary conditions are given in terms of the eigenvalues of an associated finite difference problem. When r is sufficien ly smooth, the lower bounds converge to the eigenvalues themselves as the mesh size approaches zero. A certain class of selfl equations containing no mixed derivatives is also treated. Upper bounds for the eigenvalues of a differential operator can always be found by the Rayleigh-Ritz method. That is, one puts piecewise differentiable functions vanishing on the boundary into the Poincare inequality. It was pointed out by Courant that in the case of second order operators one can reduce the problem of upper bounds to a finite difference eigenvalue adjoint systems of elliptic differential equations containing no mixed derivatives is also treated. Upper bounds for the eigenvalues of a differential operator can always be found by the Rayleigh-Ritz method. That is, one puts piecewise differentiable functions vanishing on the boundary into the Poincare inequality. It was pointed out by Courant that in the case of second order operators one can reduce the problem of upper bounds to a finite difference eigenvalue problem by using piecewise linear functions. (Author).
Download or read book Bounds for Eigenvalues and the Method of Intermediate Problems written by A. Weinstein and published by . This book was released on 1960 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book The Eigenvalue Problem for a Non self adjoint Differential Operator on the Interval pi written by Robert Richard Dingle Kemp and published by . This book was released on 1956 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Theory and Differential Operators written by E. Brian Davies and published by Cambridge University Press. This book was released on 1995 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.
Download or read book Bounds for the Eigenvalues of a Matrix written by Kenneth R. Garren and published by . This book was released on 1968 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Theory of Lower Bounds for Eigenvalues written by Hans F. Weinberger and published by . This book was released on 1959 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: A polynomial equation whose roots are lower bounds for the eigenvalues of a differential operator is derived. The coefficients of the equation depend upon some arbitrary functions and upon the minimal information necessary to determine any lower bounds. Conditions are given under which the lower bounds so obtained converge to the correct eigenvalues as more arbitrary functions are used. The method serves to unify and improve many of the known methods of finding lower bounds.
Download or read book The Princeton Companion to Applied Mathematics written by Nicholas J. Higham and published by Princeton University Press. This book was released on 2015-09-15 with total page 1031 pages. Available in PDF, EPUB and Kindle. Book excerpt: The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
Download or read book KWIC Index for Numerical Algebra written by Alston Scott Householder and published by . This book was released on 1972 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Value Problems for Operator Differential Equations written by Myroslav L. Gorbachuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1970 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relative Eigenvalue Problems for Ordinary Differential Operators written by Charles Edward Hughes and published by . This book was released on 1970 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
