Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method (Frontiers in Mathematics) - Softcover
Book 3 of 48: Frontiers in Mathematics
Synopsis
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.
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Review
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“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)
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Infinite Matrices and their Finite Sections
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 191 pp. Englisch. Seller Inventory # 9783764377663
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Condition: New. An introduction to a fascinating topic at the interface of functional analysis, algebra and numerical analysis, written for students, researchers and practitioners. This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. Series: Frontiers in Mathematics. Num Pages: 206 pages, 12 black & white illustrations, biography. BIC Classification: PB. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 244 x 170 x 11. Weight in Grams: 347. . 2006. Paperback. . . . . Seller Inventory # V9783764377663
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Condition: New. An introduction to a fascinating topic at the interface of functional analysis, algebra and numerical analysis, written for students, researchers and practitioners. This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. Series: Frontiers in Mathematics. Num Pages: 206 pages, 12 black & white illustrations, biography. BIC Classification: PB. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 244 x 170 x 11. Weight in Grams: 347. . 2006. Paperback. . . . . Books ship from the US and Ireland. Seller Inventory # V9783764377663