The structure of functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2001
|
| Series: | Monographs in mathematics
97 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 425 S. graph. Darst. |
| ISBN: | 3764365463 9783764365462 9783034805681 |
Staff View
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Record in the Search Index
| _version_ | 1804128579431170048 |
|---|---|
| adam_text | HANS TRIEBEL THE STRUCTURE OF FUNCTIONS BIRKHAUSER VERLAG BASEL * BOSTON
* BERLIN CONTENTS PREFACE XI I DECOMPOSITIONS OF FUNCTIONS 1
INTRODUCTION, HEURISTICS, AND PRELIMINARIES 1 CLASSICAL FUNCTION SPACES;
QUARKONIAL REPRESENTATIONS; WEIERSTRASSIAN APPROACH 2 SPACES ON M N :
THE REGULAR CASE 10 SEQUENCE SPACES B PQ AND F PQ ; /3-QUARKS; BP Q (R N
) WITH S A P AND FP Q (M. N ) WITH S A PQ ; UNCONDITIONAL
CONVERGENCE AND OPTIMAL COEFFICIENTS; WEIERSTRASSIAN APPROACH AND CAUCHY
FORMULA; GENERALIZED QUARKS 3 SPACES ON R N : THE GENERAL CASE 27
/3-QUARKS; B* Q (R N ) AND F Q (R N ) WITH S R; OPTIMAL COEFFICIENTS
AND WEIERSTRASSIAN APPROACH 4 AN APPLICATION: THE FUBINI PROPERTY 34
DEFINITION; THEOREM 5 SPACES ON DOMAINS: LOCALIZATION AND HARDY
INEQUALITIES 41 DEFINITION OF A SPQ (N), A SPQ (TY, ^(FT) WITH A = B OR
A = F; RELATIONS BETWEEN THESE SPACES; DENSITY ASSERTIONS; HARDY
INEQUALITIES FOR F^-SPACES; HARDY INEQUALITIES FOR BP Q -SPACES; REFINED
LOCALIZATION FOR FP Q (L) SPACES WITH S A PQ ; EQUIVALENT QUASI-NORMS
FOR .F^-SPACES; POINTWISE MULTIPLIERS; APPROXIMATE RESOLUTIONS OF UNITY;
REFINED LOCALIZATION FOR OTHER CASES 6 SPACES ON DOMAINS: DECOMPOSITIONS
71 APPROXIMATE RESOLUTIONS OF UNITY; /3-QUARKS; SEQUENCE SPACES;
QUARKONIAL DECOMPOSITIONS FOR .F^-SPACES ON DOMAINS; UNCONDITIONAL
CONVERGENCE AND OPTIMAL COEFFICIENTS; ALTERNATIVE APPROACH; REFERENCES
VI CONTENTS 7 SPACES ON MANIFOLDS 81 RIEMANNIAN MANIFOLDS (M, G) WITH
BOUNDED GEOMETRY AND POSITIVE INJECTIVITY RADIUS; (I-DOMAINS; RESOLUTION
OF UNITY; THE SPACES F PQ (M,G X ); REFINED LOCALIZATIONS;
LAPLACE-BELTRAMI OPERATOR AND RELATED LIFTS; EMBEDDINGS; FAMILIES OF
APPROXIMATE RESOLUTIONS OF UNITY; /3-QUARKS; QUARKONIAL DECOMPOSITIONS
OF F PQ {M,G*); OPTIMAL COEFFICIENTS 8 TAYLOR EXPANSIONS OF
DISTRIBUTIONS 101 WEIGHTED SPACES AND TEMPERED DISTRIBUTIONS IN E N ;
RELATED /3-QUARKS; QUARKONIAL DECOMPOSITIONS OF WEIGHTED B^-SPACES ON
E ; QUARKONIAL DECOMPOSITIONS AND TAYLOR EXPANSIONS OF TEMPERED
DISTRIBUTIONS ON R N ; TEMPERED DISTRIBUTIONS IN DOMAINS; RELATED
/3-QUARKS; QUARKONIAL DECOMPOSITIONS AND TAYLOR EXPANSIONS OF TEMPERED
DISTRIBUTIONS ON DOMAINS 9 TRACES ON SETS, RELATED FUNCTION SPACES AND
THEIR DECOMPOSITIONS 120 FINITE COMPACTLY SUPPORTED RADON MEASURES IN R*
AS DISTRIBUTIONS; TRACE OPERATOR AND IDENTIFICATION OPERATOR; LOCAL
MEANS; CRITERIA FOR THE EXISTENCE OF TRACES OF F PQ (M. N ) ON COMPACT
SETS; RELATED POTENTIALS AND MAXIMAL FUNCTIONS; TRACE SPACES; RELATED
COMMENTS AND REFERENCES; BALL CONDITION; CRITERION FOR SETS SATISFYING
THE BALL CONDITION; TRACES ON SETS SATISFYING THE BALL CONDITION;
APPROXIMATE LATTICES AND SUBORDINATED RESOLUTIONS OF UNITY ON COMPACT
SETS; /3-QUARKS ON SETS; .B^-SPACES ON SETS AND RELATED QUARKONIAL
DECOMPOSITIONS; TRACE SPACES ON SETS; COMMENTS AND REFERENCES II SHARP
INEQUALITIES 10 INTRODUCTION: OUTLINE OF METHODS AND RESULTS 161
PRELIMINARY VERSIONS OF: REARRANGEMENTS; THREE CASES: SUB-CRITICAL,
CRITICAL, SUPER-CRITICAL; GROWTH AND CONTINUITY ENVELOPES AND ENVELOPE
FUNCTIONS; RELATED BOREL MEASURES ON THE REAL LINE; RELATED HARDY
INEQUALITIES 11 CLASSICAL INEQUALITIES 167 SHARP EMBEDDINGS OF B Q (R N
) AND F^ Q (R N ) IN: L[ OC (R N ), L R (R N ), C(R N ), C-^R*);
LORENTZ-ZYGMUND SPACES; SHARP REFINED CLASSICAL EMBEDDINGS IN LIMITING
SITUATIONS OF BP Q (R N ) AND H P (R N ) IN LORENTZ SPACES AND ZYGMUND
SPACES AND RELATED INEQUALITIES; HISTORICAL COMMENTS AND REFERENCES
CONTENTS VII 12 ENVELOPES 181 REARRANGEMENT AND GROWTH FUNCTIONS;
RELATED BOREL MEASURES ON THE REAL LINE; EXAMPLES OF ADMITTED BOREL
MEASURES; GROWTH ENVELOPE FUNCTIONS; EQUIVALENCE CLASSES OF GROWTH
ENVELOPE FUNCTIONS; GROWTH ENVELOPES; RELATED INEQUALITIES; MODULI OF
CONTINUITY; CONTINUITY ENVELOPE FUNCTIONS; EQUIVALENCE CLASSES OF
CONTINUITY ENVELOPE FUNCTIONS; CONTINUITY ENVELOPES; INEQUALITIES
BETWEEN MODULI OF CONTINUITY AND REARRANGEMENTS 13 THE CRITICAL CASE 202
N N CALCULATION OF THE GROWTH ENVELOPES ^.CB PQ AND &QF PQ ; RELATED
INEQUALITIES; EXTREMAL FUNCTIONS; HISTORICAL COMMENTS AND REFERENCES;
SPACES ON DOMAINS AND RELATED GROWTH ENVELOPES; BMO AND ITS GROWTH
ENVELOPE 14 THE SUPER-CRITICAL CASE 218 I+- I+* CALCULATION OF THE
CONTINUITY ENVELOPES (BCB PQ P AND CF PQ P ; EXTREMAL FUNCTIONS;
RELATED INEQUALITIES; BORDERLINE CASES; ENVELOPE FUNCTIONS AND
NON-COMPACTNESS; HISTORICAL COMMENTS AND REFERENCES 15 THE SUB-CRITICAL
CASE 229 CALCULATION OF THE GROWTH ENVELOPES PQ AND CF PQ IN THE
SUB-CRITICAL CASE; RELATED INEQUALITIES; OPTIMAL EMBEDDINGS IN LORENTZ
SPACES AND ZYGMUND SPACES; REFERENCES 16 HARDY INEQUALITIES 235 HARDY
INEQUALITIES AS CONSEQUENCES OF SHARP EMBEDDINGS: CRITICAL CASE,
SUB-CRITICAL CASE; REFERENCES; HARDY INEQUALITIES RELATED TO HALF-SPACE,
DOMAINS, D-SETS, BOREL MEASURES 17 COMPLEMENTS 243 GREEN S FUNCTIONS AS
ENVELOPE FUNCTIONS; FURTHER LIMITING EMBEDDINGS; MODULI OF CONTINUITY;
GENERALIZED 5-SPACES AND LIP-SPACES; LOGARITHMIC SPACES; COMPACT
EMBEDDINGS; REFERENCES III FRACTAL ELLIPTIC OPERATORS 18 INTRODUCTION
251 PRELIMINARY VERSIONS OF: D-SETS AND (D, I/)-SETS, TYPES OF FRACTAL
ELLIPTIC OPERATORS, RELATED SPECTRAL PROBLEMS 19 SPECTRAL THEORY FOR THE
FRACTAL LAPLACIAN 253 PHYSICAL AND MATHEMATICAL BACKGROUND; THE
DIRICHLET LAPLACIAN AND ITS MAPPING PROPERTIES; THE FRACTAL ELLIPTIC
OPERATORS B = (-A) 1 O TR R AND (-A) 1 O /X; DENSITY OF D(R N T) IN
SOME VIII CONTENTS FUNCTION SPACES: SPECTRAL SYNTHESIS; RELATED
REFERENCES; SPECTRAL THEORY OF THE OPERATOR B RELATED TO D-SETS:
EIGENVALUES AND EIGENFUNCTIONS; THE CASE N = 1; WEYL MEASURES; STRONGLY
DIFFUSE * MEASURES; ENTROPY NUMBERS AND APPROXIMATION NUMBERS; FRACTAL
DRUMS IN THE PLANE; THE MUSIC OF THE FERNS: WEYLIAN OR ALIEN; DEGENERATE
CASE 20 THE FRACTAL DIRICHLET PROBLEM 294 SMOOTH CASE, SINGLE LAYER
POTENTIALS; DUALITY OF .FF ^SPACES IN ARBITRARY DOMAINS; H S -SPACES ON
D-SETS; THE OPERATOR B AND SINGLE LAYER POTENTIALS ON D-SETS; MAPPING
PROPERTIES; THE FRACTAL DIRICHLET PROBLEM; REFERENCES; DIRICHLET PROBLEM
IN DOMAINS WITH FRACTAL BOUNDARY; THE SMOOTH CASE; L 2 - P -THEORY;
CLASSICAL SOLUTIONS, WIENER CRITERION 21 SPECTRAL THEORY ON MANIFOLDS
310 CONTINUATION OF SECT. 7: RIEMANNIAN MANIFOLDS M, FUNCTION SPACES F
PQ (M,G H ), COMPACT EMBEDDINGS, RELATED ENTROPY NUMBERS; THE OPERATOR
HP = * A G + GID * F3G~*; CALCULATION OF THE NEGATIVE SPECTRUM OF HP;
LOCAL SINGULARITIES AND HYDROGEN-LIKE OPERATORS, RELATED ENTROPY NUMBERS
AND NEGATIVE SPECTRA; THE OPINION OF THE PHYSICISTS IN SUCH HYPERBOLIC
WORLDS 22 ISOTROPIC FRACTALS AND RELATED FUNCTION SPACES 329 ANALYSIS
VERSUS (FRACTAL) GEOMETRY; (D, I/)-SETS AND PROPERTIES OF ADMISSIBLE
FUNCTIONS T; RELATED MEASURES ARE WEYL MEASURES; PSEUDO SELF-SIMILAR
SETS AND TPIFS; FUNCTION SPACES OF TYPE B^(R N ) AND ^ ^(R*); RELATED
ATOMS, /3-QUARKS, AND QUARKONIAL DECOMPOSITIONS; TAILORED SPACES FOR (D,
*)-SETS; SPACES ON (D, I/)-SETS AND RELATED ENTROPY NUMBERS 23
ISOTROPIC FRACTAL DRUMS 348 EXTENSION OF THE SPECTRAL THEORY IN SECT. 19
FROM D-SETS TO (D, 5 F )-SETS; WEYL MEASURES IV TRUNCATIONS AND
SEMI-LINEAR EQUATIONS 24 INTRODUCTION 355 PRELIMINARY VERSIONS:
TRUNCATION PROPERTY, TRUNCATION COUPLE, Q-OPERATOR, SEMI-LINEAR
EQUATIONS 25 TRUNCATIONS 357 REAL SPACES B G (R N ), F G (R N ), M(R
N ); TRUNCATION OPERATORS T, T + ; EXAMPLES; FATOU PROPERTY; TRUNCATION
PROPERTY, UNIFORM CONTENTS CONTINUITY; TRUNCATION COUPLES; CALCULATION
OF ALL TRUNCATION COUPLES; TRUNCATION PROPERTY FOR FP G (]R N );
NON-LINEAR INTERPOLATION; REFERENCES; TRUNCATION PROPERTY FOR H(R N )
AND BMO(R N ); LIPSCHITZ-CONTINUITY; HOLDER-CONTINUITY 26 THE Q-OPERATOR
385 DEFINITION OF THE Q-OPERATOR; PROPERTIES: BOUNDEDNESS AND
LIPSCHITZ-CONTINUITY 27 SEMI-LINEAR EQUATIONS; THE Q-METHOD 389
SEMI-LINEAR INTEGRAL EQUATIONS AND RELATED REGULARITY THEORY: THE
Q-METHOD; SEMI-LINEAR DIFFERENTIAL EQUATIONS AND RELATED REGULARITY
THEORY; LOCAL SINGULARITIES AND RELATED REGULARITY THEORY; THE Q-METHOD
REVISITED REFERENCES 403 SYMBOLS 419 INDEX 423 T. M
|
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| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV013757570 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:51:29Z |
| institution | BVB |
| isbn | 3764365463 9783764365462 9783034805681 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009405640 |
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| physical | XII, 425 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Triebel, Hans 1936- Verfasser (DE-588)133515923 aut The structure of functions Hans Triebel Basel [u.a.] Birkhäuser 2001 XII, 425 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics 97 Hier auch später erschienene, unveränderte Nachdrucke Fraktal Funktionenraum Wavelet Fractals Function spaces Wavelets (Mathematics) Fraktal (DE-588)4123220-3 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Funktionenraum (DE-588)4134834-5 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 DE-604 Monographs in mathematics 97 (DE-604)BV000008284 97 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009405640&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Triebel, Hans 1936- The structure of functions Monographs in mathematics Fraktal Funktionenraum Wavelet Fractals Function spaces Wavelets (Mathematics) Fraktal (DE-588)4123220-3 gnd Wavelet (DE-588)4215427-3 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4123220-3 (DE-588)4215427-3 (DE-588)4134834-5 |
| title | The structure of functions |
| title_auth | The structure of functions |
| title_exact_search | The structure of functions |
| title_full | The structure of functions Hans Triebel |
| title_fullStr | The structure of functions Hans Triebel |
| title_full_unstemmed | The structure of functions Hans Triebel |
| title_short | The structure of functions |
| title_sort | the structure of functions |
| topic | Fraktal Funktionenraum Wavelet Fractals Function spaces Wavelets (Mathematics) Fraktal (DE-588)4123220-3 gnd Wavelet (DE-588)4215427-3 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Fraktal Funktionenraum Wavelet Fractals Function spaces Wavelets (Mathematics) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009405640&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008284 |
| work_keys_str_mv | AT triebelhans thestructureoffunctions |