Functional Analysis I: Linear Functional Analysis: 19 (Encyclopaedia of Mathematical Sciences) - Tapa blanda
Sinopsis
EMS 19 is the only Encyclopaedia volume in Functional Analysis that will appear in the foreseeable future. It is a general survey of the field, covering both the classical and modern approaches. Because of the widespread use of functional analysis in other parts of mathematics, this volume complements the volumes in the other four Encyclopaedia subseries in analysis. The material is particularly well-presented, giving first the applications and classical techniques, then covering the modern theory, thus reversing the usual order of theory first, applications second.
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Reseña del editor
The twentieth-century view of the analysis of functions is dominated by the study of classes of functions. 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.
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 296 pp. Englisch. Nº de ref. del artículo: 9783642080708
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Functional Analysis I
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Taschenbuch. Condición: Neu. Functional Analysis I | Linear Functional Analysis | Yu. I. Lyubich | Taschenbuch | V | Englisch | 2010 | Springer | EAN 9783642080708 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Nº de ref. del artículo: 107167395
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Functional Analysis I
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ISBN 10: 3642080707
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Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 296 pp. Englisch. Nº de ref. del artículo: 9783642080708
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Functional Analysis I : Linear Functional Analysis
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ISBN 10: 3642080707
ISBN 13: 9783642080708
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