Infinite Matrices and their Finite Sections (Paperback)

Marko Lindner

ISBN 10: 3764377666 / ISBN 13: 9783764377663

Published by Birkhauser Verlag AG, Basel, 2006

About this Item

Paperback. In this book we are concerned with the study of a certain class of in?nite matrices and two important properties of them: their Fredholmness and the stability of the approximation by their ?nite truncations. Let us take these two properties as a starting point for the big picture that shall be presented in what follows. Stability Fredholmness We think of our in?nite matrices as bounded linear operators on a Banach space E of two-sided in?nite sequences. Probably the simplest case to start with 2 +? is the space E = of all complex-valued sequences u=(u ) for which m m=?? 2 |u | is summable over m? Z. m Theclassofoperatorsweareinterestedinconsistsofthoseboundedandlinear operatorsonE whichcanbeapproximatedintheoperatornormbybandmatrices. We refer to them as band-dominated operators. Of course, these considerations 2 are not limited to the space E = . We will widen the selection of the underlying space E in three directions: p We pass to the classical sequence spaces with 1? p?? n Our elements u=(u )? E have indices m? Z rather than just m? Z. m We allow values u in an arbitrary ?xed Banach spaceX rather than C. is the space E = of all complex-valued sequences u=(u ) for which m m=?? We will widen the selection of the underlying space E in three directions: p We pass to the classical sequence spaces with 1? Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783764377663

Bibliographic Details

• Title: Infinite Matrices and their Finite Sections (Paperback)
• Publisher: Birkhauser Verlag AG, Basel
• Publication Date: 2006
• Language: English
• ISBN 10: 3764377666
• ISBN 13: 9783764377663
• Binding: Paperback
• Condition: new

About this title

Synopsis

This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. The main concepts presented are invertibility at infinity (closely related to Fredholmness), limit operators, and the stability and convergence of finite matrix approximations. Concrete examples are used to illustrate the results throughout, including discrete Schrödinger operators and integral and boundary integral operators arising in mathematical physics and engineering.

Review

From the reviews:

“The book under review introduces the reader to one of the central themes concerning infinite matrices: approximation by matrices of finite size. It is written for a broad audience starting with graduate students in mathematics and above. ... It is more introductory in nature and provides a very accessible summary of core themes, which are helpful in understanding properties of infinite matrices like Fredholmness, invertibility at infinity, stability and limit operators.” (G. Feichtinger, Monatshefte für Mathematik, Vol. 159 (4), March, 2010)