TY - BOOK ID - 5451456 TI - Infinite matrices and their finite sections : an introduction to the limit operator method. PY - 2006 SN - 9783764377663 3764377666 9786611343316 1281343315 3764377674 PB - Basel Birkhäuser DB - UniCat KW - Infinite matrices. KW - Linear operators. KW - Numerical analysis. KW - Integral equations. KW - Matrices infinies KW - Opérateurs linéaires KW - Analyse numérique KW - Equations intégrales KW - Infinite matrices. » More like this Linear operators. » More like this Numerical analysis. » More like this Integral equations. KW - Infinite matrices KW - Linear operators KW - Numerical analysis KW - Integral equations KW - Algebra KW - Calculus KW - Mathematics KW - Physical Sciences & Mathematics KW - 517.98 KW - Functional analysis and operator theory KW - 517.98 Functional analysis and operator theory KW - Equations, Integral KW - Matrices, Infinite KW - Linear maps KW - Maps, Linear KW - Operators, Linear KW - Mathematics. KW - Matrix theory. KW - Algebra. KW - Functional analysis. KW - Functional Analysis. KW - Linear and Multilinear Algebras, Matrix Theory. KW - Numerical Analysis. KW - Mathematical analysis KW - Operator theory KW - Functional equations KW - Functional analysis KW - Matrices KW - Functional calculus KW - Calculus of variations UR - https://www.unicat.be/uniCat?func=search&query=sysid:5451456 AB - 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. ER -