The Structure of Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2001
|
| Schriftenreihe: | Monographs in Mathematics
97 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m) : m E zn} is a resolution of unity in ]R. n. Let 'IjJ!3(x) = x!3'IjJ(x) where x E ]R. n and {3 E N~. One may ask under which circumstances functions and distributions f in ]R. n admit expansions 00 (0. 1) f(x) = L L L ). . ~m'IjJ!3(2jx - m), x E ]R. n, n !3ENg j=O mEZ with the coefficients ). . ~m E C. This resembles, at least formally, the Weier strassian approach to holomorphic functions (in the complex plane), combined with the wavelet philosophy: translations x 1---4 x - m where m E zn and dyadic j dilations x 1---4 2 x where j E No in ]R. n. Such representations pave the way to constructive definitions offunction spaces |
| Beschreibung: | 1 Online-Ressource (XII, 425 p) |
| ISBN: | 9783034882576 9783034894944 |
| DOI: | 10.1007/978-3-0348-8257-6 |
Internformat
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Datensatz im Suchindex
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| author | Triebel, Hans |
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| author_sort | Triebel, Hans |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8257-6 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034882576 9783034894944 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857498 |
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| publishDate | 2001 |
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| publisher | Birkhäuser Basel |
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| series2 | Monographs in Mathematics |
| spelling | Triebel, Hans Verfasser aut The Structure of Functions by Hans Triebel Basel Birkhäuser Basel 2001 1 Online-Ressource (XII, 425 p) txt rdacontent c rdamedia cr rdacarrier Monographs in Mathematics 97 This book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m) : m E zn} is a resolution of unity in ]R. n. Let 'IjJ!3(x) = x!3'IjJ(x) where x E ]R. n and {3 E N~. One may ask under which circumstances functions and distributions f in ]R. n admit expansions 00 (0. 1) f(x) = L L L ). . ~m'IjJ!3(2jx - m), x E ]R. n, n !3ENg j=O mEZ with the coefficients ). . ~m E C. This resembles, at least formally, the Weier strassian approach to holomorphic functions (in the complex plane), combined with the wavelet philosophy: translations x 1---4 x - m where m E zn and dyadic j dilations x 1---4 2 x where j E No in ]R. n. Such representations pave the way to constructive definitions offunction spaces Mathematics Mathematics, general Mathematik Funktionenraum (DE-588)4134834-5 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Funktionenraum (DE-588)4134834-5 s Fraktal (DE-588)4123220-3 s Wavelet (DE-588)4215427-3 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-8257-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Triebel, Hans The Structure of Functions Mathematics Mathematics, general Mathematik Funktionenraum (DE-588)4134834-5 gnd Wavelet (DE-588)4215427-3 gnd Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4134834-5 (DE-588)4215427-3 (DE-588)4123220-3 |
| title | The Structure of Functions |
| title_auth | The Structure of Functions |
| title_exact_search | The Structure of Functions |
| title_full | The Structure of Functions by Hans Triebel |
| title_fullStr | The Structure of Functions by Hans Triebel |
| title_full_unstemmed | The Structure of Functions by Hans Triebel |
| title_short | The Structure of Functions |
| title_sort | the structure of functions |
| topic | Mathematics Mathematics, general Mathematik Funktionenraum (DE-588)4134834-5 gnd Wavelet (DE-588)4215427-3 gnd Fraktal (DE-588)4123220-3 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Funktionenraum Wavelet Fraktal |
| url | https://doi.org/10.1007/978-3-0348-8257-6 |
| work_keys_str_mv | AT triebelhans thestructureoffunctions |