Functional Analysis I : Linear Functional Analysis

Yu. I. Lyubich

ISBN 10: 3540505849 / ISBN 13: 9783540505846

Editore: Springer Berlin Heidelberg, 1992

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783540505846

Dati bibliografici

• Titolo: Functional Analysis I : Linear Functional Analysis
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 3540505849
• ISBN 13: 9783540505846
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 21 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 21 millimetri di profondità
• Peso: 617 grammi

Descrizione articolo

Riassunto

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.

Contenuti

1. Classical Concrete Problems.- 2. Foundations and Methods.- Commentary on the Bibliography.- Author Index.