Unbounded Linear Operators PDF Download
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Author | : Seymour Goldberg |
Publisher | : Courier Corporation |
Total Pages | : 212 |
Release | : 2006-01-01 |
Genre | : Mathematics |
ISBN | : 0486453316 |
Download Unbounded Linear Operators Book in PDF, ePub and Kindle
This volume presents a systematic treatment of the theory of unbounded linear operators in normed linear spaces with applications to differential equations. Largely self-contained, it is suitable for advanced undergraduates and graduate students, and it only requires a familiarity with metric spaces and real variable theory. After introducing the elementary theory of normed linear spaces--particularly Hilbert space, which is used throughout the book--the author develops the basic theory of unbounded linear operators with normed linear spaces assumed complete, employing operators assumed closed only when needed. Other topics include strictly singular operators; operators with closed range; perturbation theory, including some of the main theorems that are later applied to ordinary differential operators; and the Dirichlet operator, in which the author outlines the interplay between functional analysis and "hard" classical analysis in the study of elliptic partial differential equations. In addition to its readable style, this book's appeal includes numerous examples and motivations for certain definitions and proofs. Moreover, it employs simple notation, eliminating the need to refer to a list of symbols.
Author | : C. W. Groetsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 134 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 3540399429 |
Download Stable Approximate Evaluation of Unbounded Operators Book in PDF, ePub and Kindle
Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.
Author | : Rabindranath Sen |
Publisher | : Anthem Press |
Total Pages | : 486 |
Release | : 2014-11-01 |
Genre | : Mathematics |
ISBN | : 1783083247 |
Download A First Course in Functional Analysis Book in PDF, ePub and Kindle
This book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.
Author | : K. Schmüdgen |
Publisher | : Birkhäuser |
Total Pages | : 381 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 3034874693 |
Download Unbounded Operator Algebras and Representation Theory Book in PDF, ePub and Kindle
*-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the six ties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. J1'rom the very beginning, and still today, represen tation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particu lar, the theory of locally convex spaces, the theory of von Neumann algebras, distri bution theory, single operator theory, the momcnt problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject.
Author | : Stephanus van Eijndhoven |
Publisher | : Springer |
Total Pages | : 277 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540397477 |
Download Trajectory Spaces, Generalized Functions and Unbounded Operators Book in PDF, ePub and Kindle
Author | : Christian Seifert |
Publisher | : Springer Nature |
Total Pages | : 321 |
Release | : 2022 |
Genre | : Differential equations |
ISBN | : 3030893979 |
Download Evolutionary Equations Book in PDF, ePub and Kindle
This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.
Author | : David Eric Edmunds |
Publisher | : Oxford University Press |
Total Pages | : 610 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 0198812051 |
Download Spectral Theory and Differential Operators Book in PDF, ePub and Kindle
This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.--
Author | : K. Schmüdgen |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 380 |
Release | : 1990-12-31 |
Genre | : Mathematics |
ISBN | : 311271573X |
Download Unbounded Operator Algebras and Representation Theory Book in PDF, ePub and Kindle
No detailed description available for "Unbounded Operator Algebras and Representation Theory".
Author | : Toka Diagana |
Publisher | : Nova Publishers |
Total Pages | : 110 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9781600214059 |
Download Non-Archimedean Linear Operators and Applications Book in PDF, ePub and Kindle
This self-contained book provides the reader with a comprehensive presentation of recent investigations on operator theory over non-Archimedean Banach and Hilbert spaces. This includes, non-Archimedean valued fields, bounded and unbounded linear operators, bilinear forms, functions of linear operators and one-parameter families of bounded linear operators on free branch spaces.
Author | : John K. Hunter |
Publisher | : World Scientific |
Total Pages | : 460 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 9789810241919 |
Download Applied Analysis Book in PDF, ePub and Kindle
This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor. The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.