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| Author | : Béla Szőkefalvi-Nagy |
| Publisher | : |
| Total Pages | : 44 |
| Release | : 1960 |
| Genre | : Functional analysis |
| ISBN | : |
| Author | : Calvin R. Putnam |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 177 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642859380 |
What could be regarded as the beginning of a theory of commutators AB - BA of operators A and B on a Hilbert space, considered as a dis cipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commuta tion relations occurring there. Here A and B were unbounded self-adjoint operators satisfying the relation AB - BA = iI, in some appropriate sense, and the problem was that of establishing the essential uniqueness of the pair A and B. The study of commutators of bounded operators on a Hilbert space has a more recent origin, which can probably be pinpointed as the paper of Wintner [6] {1947}. An investigation of a few related topics in the subject is the main concern of this brief monograph. The ensuing work considers commuting or "almost" commuting quantities A and B, usually bounded or unbounded operators on a Hilbert space, but occasionally regarded as elements of some normed space. An attempt is made to stress the role of the commutator AB - BA, and to investigate its properties, as well as those of its components A and B when the latter are subject to various restrictions. Some applica tions of the results obtained are made to quantum mechanics, perturba tion theory, Laurent and Toeplitz operators, singular integral trans formations, and Jacobi matrices.
| Author | : Béla Sz Nagy |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 481 |
| Release | : 2010-09-01 |
| Genre | : Mathematics |
| ISBN | : 1441960937 |
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
| Author | : Frigyes Riesz |
| Publisher | : Courier Corporation |
| Total Pages | : 528 |
| Release | : 2012-12-27 |
| Genre | : Mathematics |
| ISBN | : 0486162141 |
DIVClassic exposition of modern theories of differentiation and integration and principal problems and methods of handling integral equations and linear functionals and transformations. 1955 edition. /div
| Author | : Frigyes Riesz |
| Publisher | : |
| Total Pages | : 44 |
| Release | : 1960 |
| Genre | : Functional analysis |
| ISBN | : |
In 2007, the U.S. Department of Labor (DOL) and the U.S. Department of Defense (DoD) began a joint initiative to support the spouses of military personnel in their pursuit of portable postsecondary degrees or industry-recognized credentials. Through the Military Spouse Career Advancement Account (CAA) Demonstration, eligible spouses could obtain an account to pay for career-related education and training. Demonstration goals were to (1) help military spouses with careers and (2) encourage the retention of service members by increasing families' satisfaction with military life. Eight states received demonstration grants, which were used in substate areas where participating military bases and One-Stop Career Centers were located. DOL and DoD established demonstration guidelines about the local partnerships to be formed; which military spouses were eligible for CAAs; the types of training, education, and credentials that could be funded; the funding amount available to each spouse; and the extent of guidance that demonstration staff could give to spouses.) This report presents findings from the implementation evaluation of the Military Spouse Career Advancement Account Demonstration. Part I: Early Implementation of the Military Spouse Career Advancement Accounts Demonstration provides an overview of the demonstration and key findings about the demonstration's partnerships, early implementation experiences, marketing efforts, and other topics. Part II: Additional Findings from the Military Spouse Career Advancement Accounts Demonstration Study supplements the earlier report by providing additional information on implementation issues and quantitative information about the characteristics of participants, as well as their plans for using the CAAs for participation in education and training programs and the attainment of credentials, licenses, or certifications to support careers in high-wage, high-growth occupations.).
| Author | : A. Weinstein |
| Publisher | : Elsevier |
| Total Pages | : 322 |
| Release | : 1972-06-23 |
| Genre | : Mathematics |
| ISBN | : 9780080955988 |
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
| Author | : O.B. Bekken |
| Publisher | : Springer |
| Total Pages | : 216 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540382011 |
| Author | : Israel Gohberg |
| Publisher | : Birkhäuser |
| Total Pages | : 563 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 303488558X |
These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operator-theory text. In the selection of the material the taste and interest of the authors played an important role.
| Author | : Foias |
| Publisher | : Birkhäuser |
| Total Pages | : 647 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 3034877129 |
Classical H interpolation theory was conceived at the beginning of the century by C. Caratheodory, L. Fejer and I. Schur. The basic method, due to Schur, in solving these problems consists in applying the Mobius transform to peel off the data. In 1967, D. Sarason encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, B. Sz. Nagy and C. Foias obtained a purely geometrical extension of Sarason's results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries; starring with R. G. Douglas, P. S. Muhly and C. Pearcy, this is referred to as the commutant lifting theorem. In 1957, Z. Nehari considered an L interpolation problern which in turn encompassed the same classical interpolation problems, as well as the computation of the distance of a function f in L to H . At about the sametime as Sarason's work, V. M."
| Author | : Krzysztof Jarosz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 402 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821840614 |
This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.
