Functional Analysis I: Linear Functional Analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1992
|
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
19 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (V, 286 p) |
| ISBN: | 9783662028490 9783642080708 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-662-02849-0 |
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| 245 | 1 | 0 | |a Functional Analysis I |b Linear Functional Analysis |c by Yu. I. Lyubich ; edited by N. K. Nikol’skij |
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Datensatz im Suchindex
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662028490 9783642080708 |
| issn | 0938-0396 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858638 |
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| physical | 1 Online-Ressource (V, 286 p) |
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| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer Berlin Heidelberg |
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| series2 | Encyclopaedia of Mathematical Sciences |
| spelling | Lyubich, Yu. I. Verfasser aut Functional Analysis I Linear Functional Analysis by Yu. I. Lyubich ; edited by N. K. Nikol’skij Berlin, Heidelberg Springer Berlin Heidelberg 1992 1 Online-Ressource (V, 286 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 19 0938-0396 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 Mathematics Global analysis (Mathematics) Analysis Mathematik Nikol’skij, N. K. Sonstige oth https://doi.org/10.1007/978-3-662-02849-0 Verlag Volltext |
| spellingShingle | Lyubich, Yu. I. Functional Analysis I Linear Functional Analysis Mathematics Global analysis (Mathematics) Analysis Mathematik |
| title | Functional Analysis I Linear Functional Analysis |
| title_auth | Functional Analysis I Linear Functional Analysis |
| title_exact_search | Functional Analysis I Linear Functional Analysis |
| title_full | Functional Analysis I Linear Functional Analysis by Yu. I. Lyubich ; edited by N. K. Nikol’skij |
| title_fullStr | Functional Analysis I Linear Functional Analysis by Yu. I. Lyubich ; edited by N. K. Nikol’skij |
| title_full_unstemmed | Functional Analysis I Linear Functional Analysis by Yu. I. Lyubich ; edited by N. K. Nikol’skij |
| title_short | Functional Analysis I |
| title_sort | functional analysis i linear functional analysis |
| title_sub | Linear Functional Analysis |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik |
| url | https://doi.org/10.1007/978-3-662-02849-0 |
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