| Functional Analysis I: Linear Functional Analysis 1992 Edition Contributor(s): Lyubich, Yu I. (Author), Nikol'skij, N. K. (Editor), Tweddle, I. (Translator) |
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ISBN: 3540505849 ISBN-13: 9783540505846 Publisher: Springer OUR PRICE: $123.49 Product Type: Hardcover - Other Formats Published: February 1992 Annotation: The twentieth century view of the analysis of functions is dominated by the study of classes of functions, as contrasted with the older emphasis on the study of individual functions. Operator theory has had a similar evolution, leading to a primary role for families of operators. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach. The book consists of two chapters, the first of which deals with classical aspects of the subject, while the second presents the abstract modern theory and some of its applications. Both chapters are divided into sections which are devoted to individual topics. For each topic the origins are traced, the principal definitions and results are stated and illustrative examples for theory and applications are given. Usually proofs are omitted, although certain sections of Chapter 2 do contain some quite detailed proofs. The classical concrete problems of Chapter 1 provide motivation and examples, as well as a technical foundation, for the theory in Chapter 2. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Calculus |
| Dewey: 515.7 |
| Series: Encyclopaedia of Mathematical Sciences |
| Physical Information: 0.69" H x 6.14" W x 9.21" (1.31 lbs) 286 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Up to a certain time the attention of mathematicians was concentrated on the study of individual objects, for example, specific elementary functions or curves defined by special equations. With the creation of the method of Fourier series, which allowed mathematicians to work with 'arbitrary' functions, the individual approach was replaced by the 'class' approach, in which a particular function is considered only as an element of some 'function space'. More or less simultane- ously the development of geometry and algebra led to the general concept of a linear space, while in analysis the basic forms of convergence for series of functions were identified: uniform, mean square, pointwise and so on. It turns out, moreover, that a specific type of convergence is associated with each linear function space, for example, uniform convergence in the case of the space of continuous functions on a closed interval. It was only comparatively recently that in this connection the general idea of a linear topological space (L TS)l was formed; here the algebraic structure is compatible with the topological structure in the sense that the basic operations (addition and multiplication by a scalar) are continuous. |