Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos:
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| Format: | Book |
| Language: | English |
| Published: |
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Jena, Univ., Diss., 1998 |
| Physical Description: | 111 S. graph. Darst. 30 cm |
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MARC
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| 245 | 1 | 0 | |a Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos |c von Erich Walter Farkas |
| 264 | 1 | |c 1998 | |
| 300 | |a 111 S. |b graph. Darst. |c 30 cm | ||
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| 500 | |a Jena, Univ., Diss., 1998 | ||
| 650 | 4 | |a Funktionenraum - Fraktalgeometrie - Elliptischer Differentialoperator - Spektraltheorie | |
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| _version_ | 1812461213618012160 |
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I
CONTENTS
INTRODUCTION 1
NOTATION 8
1 THE DISTRIBUTION OF EIGENFREQUENCIES OF REGULAR ANISOTROPIC FRACTAL
DRUMS 9
1.1 MOTIVATION . 9
1.2 REGULAR ANISOTROPIC FRACTALS. 10
1.3 L,,-SPACES ON REGULAR ANISOTROPIC FRACTALS. 13
1.1 THE MAIN RESULT. M
2 DECOMPOSITIONS IN ANISOTROPIC FUNCTION SPACES 17
2.1 THE SPACES /^"(R") AND / ;'(K"). 17
2.2 LOCAL MEANS. IX
2.3 ANISOTROPIC ATOMS AND THE ATOMIC DECOMPOSITION THEOREM. 20
2.1 APPLICATION TO TRACES OF ANISOT ROPIC FUNCTION SPACES. 23
2.5 ANISOTROPIC QUARKS AND THE SUBATOMIC DECOMPOSITION THEOREM. 25
3 EIGENVALUE DISTRIBUTION OF SOME FRACTAL SEMI - ELLIPTIC OPERATORS 27
3.1 REGULAR ANISOTROPIC D-SETS IN R". 27
3.2 THE SPACES 1 ). 31
3.2.1 I HE 'T I IN I ME I HEOREM. 31
3.2.2 [RACES. 32
3.2.3 ('OMPACT NESS OF EMBEDDINGS INTO /.;,(L| 32
3.3 A MODEL FRACTAL SEMI - ELLIPTIC OPERATOR. 33
4 PROOFS 37
4.1 PROOF OF THEOREM 3.11. 37
4.2 PROOF OF THEOREM 3.12. 40
4.3 ('OMMEUTSANDCOMPLEMENTSTOTHEOREMS3.IL AND 3.12. 42
4.4 PROOFS OF THE RESULTS IN SUBSECTION 3.2.3. 44
4.5 PROOF OF THEOREM 3. HI. 50
4.6 PROOFS OF THE RESULTS IN SECTION 2.4. 56
REFERENCES 63
APPENDIX 67
APPENDIX 1: THE DISTRIBUTION OF EIGENFREQUENCIES OF ANISOTROPIC FRACTAL
DRUMS 68
1 INTRODUCTION 68
2 PRELIMINARIES 70
2.1 REGULAR ANISOT ROPIC FRACTALS. 70
2.2 THE SPACES /.,.(! ). 74
3 THE MAIN RESULT
76
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/956664644
A
('() STEMS
4 PREREQUISITES FOR THE PROOF
.}.! BASIC FACTS ABOUT ENTROPY IM NI.ERS AND APPROXIMATION MIMHERS.
4.2 COMPACT NESS OL EMBEDDING' N'O
/.MI .,.
5 PROOF OF THEOREM 3.1
APPENDIX 2: ATOMIC AND SUBATOMIC DECOMPOSITIONS IN ANISOTROPIC FUNCTION
SPACES
1 INTRODUCTION
2 DEFINITIONS AND BASIC FACTS
2.1 NOTATION.
2.2 ANISOTROPIC DISTANCE INNCTIOI,-.
2.3 ANISOTROPIC INNCTION -PACE-.
3 THE MAIN RESULTS
3.1 ANISOTROPIC ATOM- AND THE A'OMIC LECOMPOSITION THEOREM.
3.2 ANISOT ROPIC (JUARKS AND THE -NBATOMIC DECOMPOSITION THEOREM.
4 RESULTS ON ANISOTROPIC FUNCTION SPACES
|.L PREREQUISITES .
1.2 PIIUIVALENL |IL;I-I NORM- .
1.3 (IEIIERAL CHARAEI M I -AT I* N .'.
1.1 LOCAL MEANS.
5 PROOFS
5.1 PROOF OL T HE A I OMIC R LEI A MI PII ION THEOREM.
5.2 PROOF OF T HE SOL ATOINIC DECONIIIION THEOREM.
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| institution | BVB |
| language | English |
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| physical | 111 S. graph. Darst. 30 cm |
| publishDate | 1998 |
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| spelling | Farkas, Erich Walter 1967- Verfasser (DE-588)121163431 aut Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos von Erich Walter Farkas 1998 111 S. graph. Darst. 30 cm txt rdacontent n rdamedia nc rdacarrier Jena, Univ., Diss., 1998 Funktionenraum - Fraktalgeometrie - Elliptischer Differentialoperator - Spektraltheorie (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008867799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farkas, Erich Walter 1967- Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos Funktionenraum - Fraktalgeometrie - Elliptischer Differentialoperator - Spektraltheorie |
| subject_GND | (DE-588)4113937-9 |
| title | Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos |
| title_auth | Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos |
| title_exact_search | Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos |
| title_full | Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos von Erich Walter Farkas |
| title_fullStr | Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos von Erich Walter Farkas |
| title_full_unstemmed | Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos von Erich Walter Farkas |
| title_short | Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic differential operatos |
| title_sort | anisotropic function spaces fractals and spectra of some elliptic and semi elliptic differential operatos |
| topic | Funktionenraum - Fraktalgeometrie - Elliptischer Differentialoperator - Spektraltheorie |
| topic_facet | Funktionenraum - Fraktalgeometrie - Elliptischer Differentialoperator - Spektraltheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008867799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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