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Regular Boundary Value Problems Associated With Pairs Of Ordinary Differential Expressions
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Book Synopsis Regular Boundary Value Problems Associated with Pairs of Ordinary Differential Expressions by : E. A. Coddington
Download or read book Regular Boundary Value Problems Associated with Pairs of Ordinary Differential Expressions written by E. A. Coddington and published by Springer. This book was released on 2006-11-15 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that two hermitian n x n matrices K, H, where H is positive definite, H> 0, can be simultaneously diagonalized. The key to the proof is to consider C[superscript]n, where C is the complex number field, as a Hilbert space [Fraktur capital]H [subscript]H with the inner product given by (f, g) = g*Hf, where f, g [lowercase Greek]Epsilon C[superscript]n, considered as a space of column vectors. Then the operator A = H−1K is selfadjoint in [Fraktur capital]H [subscript]H, and the spectral theorem readily yields the result. Of course such A, when K is not hermitian, can also be investigated in [Fraktur capital]H [subscript]H. We consider a similar problem where K, H are replaced by a pair of ordinary differential expressions L and M, where M> 0 in some sense. Two difficulties arise: (1) there are many natural choices for a selfadjoint H> 0 generated by M, and hence many choices for [Fraktur capital]H [subscript]H, and (2), once a choice for H has been made, there are many choices for the analogue of A. In our work we consider all possible choices for H> 0 and the analogue of A.
Book Synopsis Regular Boundary Value Problems Associated with Pairs of Ordinary Differential Expressions by : E. A. Coddington
Download or read book Regular Boundary Value Problems Associated with Pairs of Ordinary Differential Expressions written by E. A. Coddington and published by Lecture Notes in Mathematics. This book was released on 1981-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that two hermitian n x n matrices K, H, where H is positive definite, H > 0, can be simultaneously diagonalized. The key to the proof is to consider C[superscript]n, where C is the complex number field, as a Hilbert space [Fraktur capital]H [subscript]H with the inner product given by (f,g) = g*Hf, where f,g [lowercase Greek]Epsilon C[superscript]n, considered as a space of column vectors. Then the operator A = H−1K is selfadjoint in [Fraktur capital]H [subscript]H, and the spectral theorem readily yields the result. Of course such A, when K is not hermitian, can also be investigated in [Fraktur capital]H [subscript]H. We consider a similar problem where K, H are replaced by a pair of ordinary differential expressions L and M, where M > 0 in some sense. Two difficulties arise: (1) there are many natural choices for a selfadjoint H > 0 generated by M, and hence many choices for [Fraktur capital]H [subscript]H, and (2), once a choice for H has been made, there are many choices for the analogue of A. In our work we consider all possible choices for H > 0 and the analogue of A.
Book Synopsis Boundary Value Problems, Weyl Functions, and Differential Operators by : Jussi Behrndt
Download or read book Boundary Value Problems, Weyl Functions, and Differential Operators written by Jussi Behrndt and published by Springer Nature. This book was released on 2020-01-03 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Ordinary Differential Equations and Operators by : W.N. Everitt
Download or read book Ordinary Differential Equations and Operators written by W.N. Everitt and published by Springer. This book was released on 2006-11-15 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Trends in Theory and Practice of Nonlinear Differential Equations by : V. Lakshmikantham
Download or read book Trends in Theory and Practice of Nonlinear Differential Equations written by V. Lakshmikantham and published by CRC Press. This book was released on 2020-12-17 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.
Book Synopsis Spectral Theory of Differential Operators by : I.W. Knowles
Download or read book Spectral Theory of Differential Operators written by I.W. Knowles and published by Elsevier. This book was released on 1981-01-01 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory of Differential Operators
Book Synopsis Partial Differential Equations and Boundary-Value Problems with Applications by : Mark A. Pinsky
Download or read book Partial Differential Equations and Boundary-Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Book Synopsis Analytic Theory of Continued Fractions by : W. B. Jones
Download or read book Analytic Theory of Continued Fractions written by W. B. Jones and published by Springer. This book was released on 2006-11-17 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Nonlinear Equations by : E.L. Allgöwer
Download or read book Numerical Solution of Nonlinear Equations written by E.L. Allgöwer and published by Springer. This book was released on 2006-11-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Developments in the Algebraic, Analytical, and Topological Theory of Semigroups by : K.H. Hofmann
Download or read book Recent Developments in the Algebraic, Analytical, and Topological Theory of Semigroups written by K.H. Hofmann and published by Springer. This book was released on 2006-11-15 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Billingsley Dimension in Probability Spaces by : H. Cajar
Download or read book Billingsley Dimension in Probability Spaces written by H. Cajar and published by Springer. This book was released on 2006-11-14 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non Commutative Harmonic Analysis and Lie Groups by : J. Carmona
Download or read book Non Commutative Harmonic Analysis and Lie Groups written by J. Carmona and published by Springer. This book was released on 2006-11-14 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Measure Theory, Oberwolfach 1981 by : D. Kölzow
Download or read book Measure Theory, Oberwolfach 1981 written by D. Kölzow and published by Springer. This book was released on 2006-12-08 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Banach Spaces, Harmonic Analysis, and Probability Theory by : R. C. Blei
Download or read book Banach Spaces, Harmonic Analysis, and Probability Theory written by R. C. Blei and published by Springer. This book was released on 2006-11-15 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry in the Large by : Heinz Hopf
Download or read book Differential Geometry in the Large written by Heinz Hopf and published by Springer. This book was released on 2013-11-11 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes consist of two parts: 1) Selected Topics in Geometry, New York University 1946, Notes by Peter Lax. 2) Lectures on Differential Geometry in the Large, Stanford University 1956, Notes by J. W. Gray. They are reproduced here with no essential change. Heinz Hopf was a mathematician who recognized important mathema tical ideas and new mathematical phenomena through special cases. In the simplest background the central idea or the difficulty of a problem usually becomes crystal clear. Doing geometry in this fashion is a joy. Hopf's great insight allows this approach to lead to serious ma thematics, for most of the topics in these notes have become the star ting-points of important further developments. I will try to mention a few. It is clear from these notes that Hopf laid the emphasis on poly hedral differential geometry. Most of the results in smooth differen tial geometry have polyhedral counterparts, whose understanding is both important and challenging. Among recent works I wish to mention those of Robert Connelly on rigidity, which is very much in the spirit of these notes (cf. R. Connelly, Conjectures and open questions in ri gidity, Proceedings of International Congress of Mathematicians, Hel sinki 1978, vol. 1, 407-414 ) • A theory of area and volume of rectilinear'polyhedra based on de compositions originated with Bolyai and Gauss.
Book Synopsis Iterative Solution of Nonlinear Systems of Equations by : R. Ansorge
Download or read book Iterative Solution of Nonlinear Systems of Equations written by R. Ansorge and published by Springer. This book was released on 2006-11-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
Book Synopsis Probability in Banach Spaces IV by : A. Beck
Download or read book Probability in Banach Spaces IV written by A. Beck and published by Springer. This book was released on 2006-11-15 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
