Function spaces of generalised smoothness:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2001
|
| Schriftenreihe: | Dissertationes mathematicae
398 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 88 S. |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Function spaces of generalised smoothness
Autor: Moura, Susana
Jahr: 2001
CONTENTS
Introduction..........................................................................................................................................................5
1. Function spaces on Rn................................................................................................................................6
1.1. Introduction............................................................................................................................................G
1.2. Definitions and basic properties......................................................................................................6
1.2.1. Basic notations..........................................................................................................................6
1.2.2. Definitions..................................................................................................................................8
1.2.3. Equivalent quasi-norms..........................................................................................................11
1.2.4. Lifting property........................................................................................................................12
1.2.5. Embeddings................................................................................................................................13
1.3. Characterisation by local means......................................................................................................14
1.4. Atomic and subatomic decompositions........................................................................................30
2. Function spaces on fractals........................................................................................................................53
2.1. (d,^)-sets................................................................................................................................................53
2.1.1. Introduction................................................................................................................................53
2.1.2. Definition and properties of a (d,l^)-set..........................................................................54
2.2. Spaces on (cf, Jf^-sets............................................................................................................................60
2.2.1. Lp(r) as spaces of distributions..........................................................................................GO
2.2.2. Traces............................................................................................................................................62
3. Entropy numbers............................................................................................................................................66
3.1. Definition and elementary properties............................................................................................66
3.2. Entropy numbers of embeddings between weighted sequence spaces................................67
3.3. Entropy numbers of embeddings between spaces on fractals................................................76
4. Applications....................................................................................................................................................82
4.1. Fractal drums........................................................................................................................................82
References..............................................................................................................................................................86
Abstract
We study spaces of generalised smoothness of Besov and Triebel-Lizorkin type. In particular,
we get characterisations by local means, atomic and subatomic representations. These results
are applied to estimate the entropy numbers of compact embeddings between function spaces
on fractals. Due to Carl s inequality this is useful in the study of the behaviour of eigenvalues in
problems which correspond to the vibrations of a drum, the whole mass of which is concentrated
on a fractal subset of the drum.
2000 Mathematics Subject Classification: 28A78, 28A80, 35P15, 46E30, 46E35, 47B06.
Received 27.7.2000; revised 11.12.2000.
Acknowledgements. It is a pleasure to thank Prof. Triebel for his helpful comments and sugges-
tions. The author takes this opportunity to gratefully acknowledge the Function Spaces research
group in Jena for their hospitality during the stays at that University.
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:01:30Z |
| institution | BVB |
| language | English |
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| oclc_num | 48948375 |
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| physical | 88 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Polska Akad. Nauk, Inst. Matematyczny |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Moura, Susana 1971- Verfasser (DE-588)142596477 aut Function spaces of generalised smoothness Susana Moura Warszawa Polska Akad. Nauk, Inst. Matematyczny 2001 88 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 398 Embeddings (Mathematics) Fractals Function spaces Smoothness of functions Dissertationes mathematicae 398 (DE-604)BV000003039 398 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009818138&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moura, Susana 1971- Function spaces of generalised smoothness Dissertationes mathematicae Embeddings (Mathematics) Fractals Function spaces Smoothness of functions |
| title | Function spaces of generalised smoothness |
| title_auth | Function spaces of generalised smoothness |
| title_exact_search | Function spaces of generalised smoothness |
| title_full | Function spaces of generalised smoothness Susana Moura |
| title_fullStr | Function spaces of generalised smoothness Susana Moura |
| title_full_unstemmed | Function spaces of generalised smoothness Susana Moura |
| title_short | Function spaces of generalised smoothness |
| title_sort | function spaces of generalised smoothness |
| topic | Embeddings (Mathematics) Fractals Function spaces Smoothness of functions |
| topic_facet | Embeddings (Mathematics) Fractals Function spaces Smoothness of functions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009818138&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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