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| Author | : Frédéric Bayart |
| Publisher | : Cambridge University Press |
| Total Pages | : 352 |
| Release | : 2009-06-04 |
| Genre | : Mathematics |
| ISBN | : 0521514967 |
The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.
| Author | : Arch W. Naylor |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 648 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : 9780387950013 |
This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.
| Author | : Nelson Dunford |
| Publisher | : Wiley |
| Total Pages | : 2648 |
| Release | : 2009-05-26 |
| Genre | : Mathematics |
| ISBN | : 9780470555613 |
This set features: Linear Operators, Part 1, General Theory (978-0-471-60848-6), Linear Operators, Part 2, Spectral Theory, Self Adjoint Operators in Hilbert Space (978-0-471-60847-9), and Linear Operators, Part 3, Spectral Operators (978-0-471-60846-2), all by Neilson Dunford and Jacob T. Schwartz.
| Author | : S. Banach |
| Publisher | : Elsevier |
| Total Pages | : 249 |
| Release | : 1987-03-01 |
| Genre | : Computers |
| ISBN | : 0080887201 |
This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.
| Author | : Aref Jeribi |
| Publisher | : CRC Press |
| Total Pages | : 270 |
| Release | : 2018-04-17 |
| Genre | : Mathematics |
| ISBN | : 135104625X |
Linear Operators and Their Essential Pseudospectra provides a comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest in the volume include various essential spectra, but the author also considers some of the generalizations that have been studied. In recent years, spectral theory has witnessed an explosive development. This volume presents a survey of results concerning various types of essential spectra and pseudospectra in a unified, axiomatic way and also discusses several topics that are new but which relate to the concepts and methods emanating from the book. The main topics include essential spectra, essential pseudospectra, structured essential pseudospectra, and their relative sets. This volume will be very useful for several researchers since it represents not only a collection of previously heterogeneous material but also includes discussions of innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many areas of mathematics, the author suggests that some modest prerequisites from functional analysis and operator theory should be in place to be accessible to newcomers and graduate students of mathematics.
| Author | : Aref Jeribi |
| Publisher | : Springer Nature |
| Total Pages | : 509 |
| Release | : 2021-07-28 |
| Genre | : Mathematics |
| ISBN | : 981162528X |
This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.
| Author | : Thomas F. Jordan |
| Publisher | : Courier Corporation |
| Total Pages | : 162 |
| Release | : 2012-09-20 |
| Genre | : Science |
| ISBN | : 0486140547 |
Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.
| Author | : Asao Arai |
| Publisher | : World Scientific |
| Total Pages | : 893 |
| Release | : 2017-12-20 |
| Genre | : Science |
| ISBN | : 9813207132 |
This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation relations and canonical anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and a short description to each model is given.To graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory, this book is a good introductory text. It is also well suited for self-study and will provide readers a firm foundation of knowledge and mathematical techniques for reading more advanced books and current research articles in the field of mathematical analysis on quantum fields. Also, numerous problems are added to aid readers to develop a deeper understanding of the field.
| Author | : Paul R. Halmos |
| Publisher | : Courier Dover Publications |
| Total Pages | : 209 |
| Release | : 2017-05-24 |
| Genre | : Mathematics |
| ISBN | : 0486822265 |
Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.
| Author | : Vasile I. Istratescu |
| Publisher | : CRC Press |
| Total Pages | : 605 |
| Release | : 2020-08-14 |
| Genre | : Mathematics |
| ISBN | : 1000146324 |
This book is an introduction to the subject and is devoted to standard material on linear functional analysis, and presents some ergodic theorems for classes of operators containing the quasi-compact operators. It discusses various classes of operators connected with the numerical range.
