Kategoria BISAC: Mathematics >> Transformations

This book presents an introduction to the theory of transformation groups which will be suitable for all those coming to the subject for the first time. The emphasis is on the study of compact Lie groups acting on manifolds. Throughout, much care is taken to illustrate concepts and results with examples and applications. Numerous exercises are also included to further extend a reader's understanding and knowledge. Prerequisites are a familiarity with algebra and topology as might have been acquired from an undergraduate degree in Mathematics. The author begins by introducing the basic...

From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem....

This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed...

The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.

The aim of this book is twofold: (i) to give an exposition of the basic theory of finite-dimensional algebras at a levelthat isappropriate for senior undergraduate and first-year graduate students, and (ii) to provide the mathematical foundation needed to prepare the reader for the advanced study of anyone of several fields of mathematics. The subject under study is by no means new-indeed it is classical- yet a book that offers a straightforward and concrete treatment of this theory seems justified for several reasons. First, algebras and linear trans- formations in one guise or another are...

In this book we study function spaces of low Borel complexity.
Techniques from general topology, infinite-dimensional topology, functional analysis and descriptive set theory
are primarily used for the study of these spaces. The mix of
methods from several disciplines makes the subject
particularly interesting. Among other things, a complete and self-contained proof of the Dobrowolski-Marciszewski-Mogilski Theorem that all function spaces of low Borel complexity are topologically homeomorphic, is presented.

In order to understand what is going on, a solid background...

Presenting an overview of most aspects of modern Banach space theory and its applications, this handbook offers up-to-date surveys by a range of expert authors. The surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory and partial differential equations. contains all the background needed for reading any other chapter. Each of the 21 articles after his is devoted to one specific direction of Banach space theory or its applications. Each article...

This classic offers a meticulous account of the theory of finite elasticity. It covers the application of the theory to the solution of boundary-value problems, as well asthe analysis of the mechanical properties of solid materials capable of large elastic deformations. Setting is purely isothermal. Problems. References. Appendixes."

Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before...

The first part of this book is an introduction with emphasis on examples that illustrate the theory of operator spaces. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third part of the book describes applications to non self-adjoint operator algebras and similarity problems. The author's counterexample to the "Halmos problem" is presented, along with work on the new concept of "length" of an operator algebra.

One service mathematics has rendered the 'Et moi, ... si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a...

This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role.

The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references...

Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis. In particular, they play a decisive role in the modem theory of partial differential equations (PDE). Potential theory, which grew out of the theory of the electrostatic or gravita tional potential, the Laplace equation, the Dirichlet problem, etc., had a fundamen tal role in the development of functional analysis and the theory of Hilbert space. Later, potential theory was strongly influenced by functional analysis. More re cently, ideas from...

This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki's Topologie generale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover."

This is the softcover reprint of the 1975 English translation of the first three chapters of Bourbaki's Groupes et algebres de Lie. The first chapter describes the theory of Lie algebras, their deviations, representations, and enveloping algebras. Chapter two introduces free Lie algebras in order to discuss the exponential, logarithmic and the Hausdorff series. Chapter three deals with the theory of Lie groups over R and C ultrametric fields.

This softcover reprint of the 1974 English translation of the first three chapters of Bourbaki's Algebre gives a thorough exposition of the fundamentals of general, linear, and multilinear algebra. The first chapter introduces the basic objects, such as groups and rings. The second chapter studies the properties of modules and linear maps, and the third chapter discusses algebras, especially tensor algebras.

This book is intended as an introduction to the theory of tensor products of Banach spaces. The prerequisites for reading the book are a first course in Functional Analysis and in Measure Theory, as far as the Radon-Nikodym theorem. The book is entirely self-contained and two appendices give addi- tional material on Banach Spaces and Measure Theory that may be unfamil- iar to the beginner. No knowledge of tensor products is assumed. Our viewpoint is that tensor products are a natural and productive way to understand many of the themes of modern Banach space theory and that "tensorial...

Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.
The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory...

This book presents a theory motivated by the spaces LP, 0 p