Non Self Adjoint Boundary Eigenvalue Problems

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Non Self Adjoint Boundary Eigenvalue Problems

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Author : R. Mennicken
language : en
Publisher: Gulf Professional Publishing
Release Date : 2003-06-26

Non Self Adjoint Boundary Eigenvalue Problems written by R. Mennicken and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Mathematics categories.

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.

Operator Theory And Boundary Eigenvalue Problems

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Author : I. Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Operator Theory And Boundary Eigenvalue Problems written by I. Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.

Sturm Liouville Theory

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Author : Anton Zettl
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Sturm Liouville Theory written by Anton Zettl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Education categories.

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.

Ordinary Differential Operators

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Author : Aiping Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-08

Ordinary Differential Operators written by Aiping Wang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-08 with Education categories.

In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.

Spectral Theory And Excitation Of Open Structures

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Author : V. P. Shestopalov
language : en
Publisher: IET
Release Date : 1996

Spectral Theory And Excitation Of Open Structures written by V. P. Shestopalov and has been published by IET this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

Open resonators, open waveguides and open diffraction gratings are used extensively in modern millimetre and submillemetre technology, spectroscopy and radio engineering. In this book, the physical processes in these open electromagnetic structures are analysed using a specially constructed spectral theory.

Mathematical Methods In Solid State And Superfluid Theory

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Author : R.C. Clark
language : en
Publisher: Springer
Release Date : 2013-12-17

Mathematical Methods In Solid State And Superfluid Theory written by R.C. Clark and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Science categories.

Asymptotics Of Elliptic And Parabolic Pdes

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Author : David Holcman
language : en
Publisher: Springer
Release Date : 2018-05-25

Asymptotics Of Elliptic And Parabolic Pdes written by David Holcman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-25 with Mathematics categories.

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.

On Lambda Nonlinear Boundary Eigenvalue Problems

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Author : Christiane Tretter
language : en
Publisher: Wiley-VCH
Release Date : 1993-09

On Lambda Nonlinear Boundary Eigenvalue Problems written by Christiane Tretter and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09 with Mathematics categories.

This book discusses nonselfadjoint (Lambda)-nonlinear boundary eigenvalue problems for ordinary differential equations. Asymptotic boundary conditions for uniform convergence of generalized eigenfunction expansions are given by a recursion and expansion theorems are established by a careful analytic study of the asymptotic behaviour of Green's function. The theory is illustrated by various examples from technical mechanics.

Functional Inequalities New Perspectives And New Applications

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Author : Nassif Ghoussoub
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-09

Functional Inequalities New Perspectives And New Applications written by Nassif Ghoussoub and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.

"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.

Waves And Fields In Inhomogenous Media

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Author : Weng Cho Chew
language : en
Publisher: John Wiley & Sons
Release Date : 1999-02-02

Waves And Fields In Inhomogenous Media written by Weng Cho Chew and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-02 with Science categories.

Electrical Engineering/Electromagnetics Waves and Fields in Inhomogeneous Media A Volume in the IEEE Press Series on Electromagnetic Waves Donald G. Dudley, Series Editor ".it is one of the best wave propagation treatments to appear in many years." Gerardo G. Tango, CPG, Consulting Seismologist-Acoustician, Covington, LA This comprehensive text thoroughly covers fundamental wave propagation behaviors and computational techniques for waves in inhomogeneous media. The author describes powerful and sophisticated analytic and numerical methods to solve electromagnetic problems for complex media and geometry as well. Problems are presented as realistic models of actual situations which arise in the areas of optics, radio wave propagation, geophysical prospecting, nondestructive testing, biological sensing, and remote sensing. Key topics covered include: * Analytical methods for planarly, cylindrically and spherically layered media * Transient waves, including the Cagniard-de Hoop method * Variational methods for the scalar wave equation and the electromagnetic wave equation * Mode-matching techniques for inhomogeneous media * The Dyadic Green's function and its role in simplifying problem-solving in inhomogeneous media * Integral equation formulations and inverse problems * Time domain techniques for inhomogeneous media This book will be of interest to electromagnetics and remote sensing engineers, physicists, scientists, and geophysicists. This IEEE Press reprinting of the 1990 version published by Van Nostrand Reinhold incorporates corrections and minor updating. Also in the series. Mathematical Foundations for Electromagnetic Theory by Donald G. Dudley, University of Arizona at Tucson This volume in the series lays the mathematical foundations for the study of advanced topics in electromagnetic theory. Important subjects covered include linear spaces, Green's functions, spectral expansions, electromagnetic source representations, and electromagnetic boundary value problems. 1994 Hardcover 264 pp ISBN 0-7803-1022-5 IEEE Order No. PC3715 About the Series The IEEE Press Series on Electromagnetic Waves consists of new titles as well as reprints and revisions of recognized classics that maintain long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, practicing engineers, and researchers, this series provides affordable volumes that explore electromagnetic waves and applications beyond the undergraduate level.