Wavelet theory:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2011
|
| Schriftenreihe: | Translations of mathematical monographs
239 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XIII, 506 S. graph. Darst. |
| ISBN: | 9780821849842 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV039559730 | ||
| 003 | DE-604 | ||
| 005 | 20181008 | ||
| 007 | t | ||
| 008 | 110901s2011 xxud||| |||| 00||| eng d | ||
| 010 | |a 2010035110 | ||
| 020 | |a 9780821849842 |c hbk. |9 978-0-8218-4984-2 | ||
| 035 | |a (OCoLC)751018054 | ||
| 035 | |a (DE-599)BVBBV039559730 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 1 | |a eng |h rus | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-703 |a DE-824 | ||
| 050 | 0 | |a QA403.3 | |
| 082 | 0 | |a 515/.2433 | |
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 100 | 1 | |a Novikov, Igorʹ Ya. |d 1958- |e Verfasser |0 (DE-588)1011706415 |4 aut | |
| 240 | 1 | 0 | |a Teorija vspleskov |
| 245 | 1 | 0 | |a Wavelet theory |c I. Ya. Novikov ; V. Yu. Protasov ; M. A. Skopina. Transl. by Evgenia Sorokina |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2011 | |
| 300 | |a XIII, 506 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 239 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Wavelets (Mathematics) | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 7 | |a Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems |2 msc | |
| 650 | 0 | 7 | |a Wavelet |0 (DE-588)4215427-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wavelet |0 (DE-588)4215427-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Protasov, Vladimir |d 1970- |e Verfasser |0 (DE-588)1011706903 |4 aut | |
| 700 | 1 | |a Skopina, Maria A. |d 1952- |e Verfasser |0 (DE-588)1011707314 |4 aut | |
| 830 | 0 | |a Translations of mathematical monographs |v 239 |w (DE-604)BV000002394 |9 239 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024411435 | ||
Datensatz im Suchindex
| _version_ | 1804148383817924608 |
|---|---|
| adam_text | Contents
Preface
їх
Chapter
1.
Wavelets on the Line
1
1.1.
Riesz bases
1
1.2.
MRA
and scaling functions
7
1.3.
Wavelet spaces
15
1.4. Haar, Battle-Lemarie,
Strömberg,
and Meyer systems
23
1.5.
Uncertainty constants
30
1.6.
Computational algorithms
40
1.7.
Convergence of wavelet expansions
42
1.8.
Wavelet frames
52
Chapter
2.
Multivariate Wavelets
63
2.1.
Separable
MRA
63
2.2.
Matrix dilation
66
2.3.
Nonseparable MRAs
69
2.4.
Construction of refinable functions
74
2.5.
Conditions of biorthogonality
79
2.6.
Construction of wavelet functions
90
2.7.
Wavelet bases
98
2.8. Haar
MRAs
105
Chapter
3.
Compactly Supported Refinable Functions
115
3.1.
Existence, uniqueness, and weak convergence
115
3.2. Strang-Fix
conditions
117
3.3.
Approximation by shifts of refinable functions
125
3.4.
Linear independence, stability, and orthogonality of integer shifts
130
3.5.
Examples and applications
140
Chapter
4.
Wavelets with Compact Support
143
4.1.
Construction of orthogonal wavelets
143
4.2.
Wavelets generated by a compactly supported scaling function
152
4.3.
Time-frequency localization
156
4.4.
Asymptotics of zeros of Bernstein s polynomials
175
Chapter
5.
Fractal Properties of Wavelets
191
5.1.
Refinable functions and fractal curves
191
5.2.
Fractal curves in the space Lp
198
5.3.
Smoothness of fractal curves in the spaces W£ and Cr
200
5.4.
Local smoothness of fractal curves
204
5.5.
Examples
216
vi
CONTENTS
Chapter
6.
Factorization of Refinement Equations
219
6.1.
Operators corresponding to the clean mask
219
6.2.
Mask cleaning procedure
222
6.3.
Space
Ãn
and the general form of the operators To, T on it
226
6.4.
Factorization theorems
231
Chapter
7.
Smoothness of Compactly Supported Wavelets
233
7.1.
Matrix method
233
7.2.
Local smoothness of wavelets
236
7.3.
Special cases and examples
241
7.4.
Method of pointwise estimation of the Fourier transform
256
7.5.
Estimation by invariant cycles
262
Chapter
8.
Nonstationary Wavelets
271
8.1.
General theory of nonstationary wavelets
271
8.2.
Nonstationary infinitely differentiable
orthonormal
wavelets
with compact support
280
8.3.
Decay rate of the Fourier transforms of elements
of a nonstationary scaling sequence
288
8.4.
Uncertainty constants for
Φ
294
8.5.
Nonstationary wavelets with modified Daubechies masks
299
8.6.
Uncertainty constants for
Φα
302
8.7.
Nonstationary wavelets bases in Sobolev spaces
305
Chapter
9.
Periodic Wavelets
315
9.1.
PMRA and scaling sequence
315
9.2.
Construction of wavelet functions
325
9.3.
Wavelet packets
330
9.4.
Generating function
332
9.5.
Kotelnikov-Shannon system
338
Chapter
10.
Approximation by Periodic Wavelets
345
10.1.
Convergence of wavelet expansions in norm
345
10.2.
Convergence of wavelet expansions almost everywhere
349
10.3.
Direct and inverse theorems
358
10.4.
Convergence of wavelet expansions at a point
370
Chapter
11.
Remarkable Properties of Wavelet Bases
381
11.1.
Unconditional wavelet bases
381
11.2.
Optimal polynomial bases in the space C(T)
390
11.3.
Optimal polynomial bases in the space C[—
1,1] 393
11.4.
Wavelet bases in
Besov
and Lizorkin-Triebel spaces
407
11.5.
Linear operators in the Lizorkin-Triebel spaces
431
Appendix A. Auxiliary Facts of the Theory of Functions
and Functional Analysis
453
A.I. Bases
453
A.
2.
Linear functionals in normed spaces
454
A.3. Distributions
455
A.4. Marcinkiewicz interpolation theorem
458
CONTENTS
vii
Α.
5.
Spectral radius
458
Α.
6.
Joint spectral radius
and the Lyapunov exponent
459
A.7.
Smoothness and the decay rate of the Fourier transform
462
A.
8.
Wiener theorem for L%
464
A.9. Lebesgue sets
465
A.
10.
Absolutely continuous functions
469
A.
11.
Nonnegative
trigonometric polynomials, Riesz s lemma
469
A.
12.
The Enestrem-Kakey theorem about zeros of polynomials
470
A.
13.
Sobolev spaces
471
A.
14.
Moduli of continuity
471
A.
15.
Approximation by trigonometric polynomials
472
A.
16.
Multidimensional Fejer means
473
A.
17.
Self-similar sets
474
A.
18.
Difference equations
475
A.
19.
Landau-Kolmogorov inequality
478
A.
20.
Legendre polynomials
478
Appendix B. Historical Comments
481
Bibliography
493
Index
505
|
| any_adam_object | 1 |
| author | Novikov, Igorʹ Ya. 1958- Protasov, Vladimir 1970- Skopina, Maria A. 1952- |
| author_GND | (DE-588)1011706415 (DE-588)1011706903 (DE-588)1011707314 |
| author_facet | Novikov, Igorʹ Ya. 1958- Protasov, Vladimir 1970- Skopina, Maria A. 1952- |
| author_role | aut aut aut |
| author_sort | Novikov, Igorʹ Ya. 1958- |
| author_variant | i y n iy iyn v p vp m a s ma mas |
| building | Verbundindex |
| bvnumber | BV039559730 |
| callnumber-first | Q - Science |
| callnumber-label | QA403 |
| callnumber-raw | QA403.3 |
| callnumber-search | QA403.3 |
| callnumber-sort | QA 3403.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)751018054 (DE-599)BVBBV039559730 |
| dewey-full | 515/.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01927nam a2200469zcb4500</leader><controlfield tag="001">BV039559730</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20181008 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110901s2011 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2010035110</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821849842</subfield><subfield code="c">hbk.</subfield><subfield code="9">978-0-8218-4984-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)751018054</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV039559730</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-824</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA403.3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.2433</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Novikov, Igorʹ Ya.</subfield><subfield code="d">1958-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1011706415</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Teorija vspleskov</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Wavelet theory</subfield><subfield code="c">I. Ya. Novikov ; V. Yu. Protasov ; M. A. Skopina. Transl. by Evgenia Sorokina</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Math. Soc.</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 506 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Translations of mathematical monographs</subfield><subfield code="v">239</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus dem Russ. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Wavelets (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wavelet</subfield><subfield code="0">(DE-588)4215427-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Wavelet</subfield><subfield code="0">(DE-588)4215427-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Protasov, Vladimir</subfield><subfield code="d">1970-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1011706903</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Skopina, Maria A.</subfield><subfield code="d">1952-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1011707314</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Translations of mathematical monographs</subfield><subfield code="v">239</subfield><subfield code="w">(DE-604)BV000002394</subfield><subfield code="9">239</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-024411435</subfield></datafield></record></collection> |
| id | DE-604.BV039559730 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:06:16Z |
| institution | BVB |
| isbn | 9780821849842 |
| language | English Russian |
| lccn | 2010035110 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024411435 |
| oclc_num | 751018054 |
| open_access_boolean | |
| owner | DE-703 DE-824 |
| owner_facet | DE-703 DE-824 |
| physical | XIII, 506 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Novikov, Igorʹ Ya. 1958- Verfasser (DE-588)1011706415 aut Teorija vspleskov Wavelet theory I. Ya. Novikov ; V. Yu. Protasov ; M. A. Skopina. Transl. by Evgenia Sorokina Providence, RI American Math. Soc. 2011 XIII, 506 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 239 Aus dem Russ. übers. Wavelets (Mathematics) Harmonic analysis Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems msc Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s DE-604 Protasov, Vladimir 1970- Verfasser (DE-588)1011706903 aut Skopina, Maria A. 1952- Verfasser (DE-588)1011707314 aut Translations of mathematical monographs 239 (DE-604)BV000002394 239 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Novikov, Igorʹ Ya. 1958- Protasov, Vladimir 1970- Skopina, Maria A. 1952- Wavelet theory Translations of mathematical monographs Wavelets (Mathematics) Harmonic analysis Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems msc Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | Wavelet theory |
| title_alt | Teorija vspleskov |
| title_auth | Wavelet theory |
| title_exact_search | Wavelet theory |
| title_full | Wavelet theory I. Ya. Novikov ; V. Yu. Protasov ; M. A. Skopina. Transl. by Evgenia Sorokina |
| title_fullStr | Wavelet theory I. Ya. Novikov ; V. Yu. Protasov ; M. A. Skopina. Transl. by Evgenia Sorokina |
| title_full_unstemmed | Wavelet theory I. Ya. Novikov ; V. Yu. Protasov ; M. A. Skopina. Transl. by Evgenia Sorokina |
| title_short | Wavelet theory |
| title_sort | wavelet theory |
| topic | Wavelets (Mathematics) Harmonic analysis Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems msc Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Wavelets (Mathematics) Harmonic analysis Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems Wavelet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT novikovigorʹya teorijavspleskov AT protasovvladimir teorijavspleskov AT skopinamariaa teorijavspleskov AT novikovigorʹya wavelettheory AT protasovvladimir wavelettheory AT skopinamariaa wavelettheory |