Author : Cornelis V. M. van der Mee
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 21,26 MB
Release : 2008-09-27
Category : Mathematics
ISBN : 3764387327
In this monograph the natural evolution operators of autonomous first-order differential equations with exponential dichotomy on an arbitrary Banach space are studied in detail. Characterizations of these so-called exponentially dichotomous operators in terms of their resolvents and additive and multiplicative perturbation results are given. This is the first book at graduate level on autonomous first-order differential equations with exponential dichotomy in a Banach space.
Author : Marinus A. Kaashoek
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 38,11 MB
Release : 2006-01-17
Category : Mathematics
ISBN : 3764373989
This book contains a selection of carefully refereed research papers, most of which were presented at the fourteenth International Workshop on Operator Theory and its Applications (IWOTA), held at Cagliari, Italy, from June 24-27, 2003. The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.
Author : Dumitru Gaspar
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 47,65 MB
Release : 2006-03-30
Category : Mathematics
ISBN : 3764373148
This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.
Author : Christiane Tretter
Publisher : Imperial College Press
Page : 297 pages
File Size : 26,56 MB
Release : 2008
Category : Mathematics
ISBN : 1848161123
This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics.
Author : Harm Bart
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 21,56 MB
Release : 2011-02-09
Category : Mathematics
ISBN : 376438753X
The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations. A large part the book deals with rational matrix functions only.
Author : Tanja Eisner
Publisher : Birkhäuser
Page : 240 pages
File Size : 23,54 MB
Release : 2016-09-24
Category : Mathematics
ISBN : 3319313835
This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main developments in the broad area of operator theory are covered, with special emphasis on applications to science and engineering. The volume also presents papers dedicated to the eightieth birthday of Damir Arov and to the sixty-fifth birthday of Leiba Rodman, both leading figures in the area of operator theory and its applications, in particular, to systems theory.
Author : Sheldon Axler
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 11,99 MB
Release : 2011-04-13
Category : Mathematics
ISBN : 3034603479
Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006. This volume is a memorial to Paul by operator theorists he inspired. Paul’sinitial research,beginning with his 1938Ph.D. thesis at the University of Illinois under Joseph Doob, was in probability, ergodic theory, and measure theory. A shift occurred in the 1950s when Paul’s interest in foundations led him to invent a subject he termed algebraic logic, resulting in a succession of papers on that subject appearing between 1954 and 1961, and the book Algebraic Logic, published in 1962. Paul’s ?rst two papers in pure operator theory appeared in 1950. After 1960 Paul’s research focused on Hilbert space operators, a subject he viewed as enc- passing ?nite-dimensional linear algebra. Beyond his research, Paul contributed to mathematics and to its community in manifold ways: as a renowned expositor, as an innovative teacher, as a tireless editor, and through unstinting service to the American Mathematical Society and to the Mathematical Association of America. Much of Paul’s in?uence ?owed at a personal level. Paul had a genuine, uncalculating interest in people; he developed an enormous number of friendships over the years, both with mathematicians and with nonmathematicians. Many of his mathematical friends, including the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, learned from his advice and his example what it means to be a mathematician.
Author : Joseph A. Ball
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 35,79 MB
Release : 2011-02-03
Category : Mathematics
ISBN : 3034601611
This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.
Author : Albrecht Böttcher
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 30,48 MB
Release : 1996
Category : Mathematics
ISBN : 082180457X
Much of the importance of mathematics lies in its ability to provide theories which are useful in widely different fields of endeavour. A good example is the large and amorphous body of knowledge known as the theory of linear operators or operator theory, which came to life about a century ago as a theory to encompass properties common to matrix, differential, and integral operators. Thus, it is a primary purpose of operator theory to provide a coherent body of knowledge which can explain phenomena common to the enormous variety of problems in which such linear operators play a part. The theory is a vital part of functional analysis, whose methods and techniques are one of the major advances of twentieth century mathematics and now play a pervasive role in the modeling of phenomena in probability, imaging, signal processing, systems theory, etc, as well as in the more traditional areas of theoretical physics and mechanics. This book is based on lectures presented at a meeting on operator theory and its applications held at the Fields Institute in 1994.
Author : Jacek Banasiak
Publisher : Springer
Page : 338 pages
File Size : 50,63 MB
Release : 2014-11-20
Category : Mathematics
ISBN : 3319121456
Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semi group theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ‘internal’ questions and in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful.
