Algebras of Approximation Sequences PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Algebras of Approximation Sequences PDF full book. Access full book title Algebras of Approximation Sequences by Steffen Roch. Download full books in PDF and EPUB format.
Author: Steffen Roch
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Steffen Roch
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Vladimir S. Rabinovich
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
Get Book Here
Book Description
Author: Steffen Roch
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Steffen Roch
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
Get Book Here
Book Description
Author: Rüdiger Göbel
Publisher: Walter de Gruyter
ISBN: 3110218119
Category : Mathematics
Languages : en
Pages : 1002
Get Book Here
Book Description
This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.
Author: Ronald Hagen
Publisher: CRC Press
ISBN: 1482270676
Category : Mathematics
Languages : en
Pages : 385
Get Book Here
Book Description
"Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. Covers fractality and Fredholmness. Explains the phenomena of the asymptotic splitting of the singular values, and more."
Author: Vladimir S. Rabinovič
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
Get Book Here
Book Description
Author: Steffen Roch
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
Get Book Here
Book Description
Author: Yann Bugeaud
Publisher: Cambridge University Press
ISBN: 1139455672
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
Book Description
An accessible and broad account of the approximation and classification of real numbers suited for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the comprehensive list of more than 600 references.
Author: Roland Hagen
Publisher: Birkhäuser
ISBN: 3034890672
Category : Mathematics
Languages : en
Pages : 388
Get Book Here
Book Description
The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.
