Orthogonal series:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
1989
|
| Schriftenreihe: | Translations of mathematical monographs
75 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | XII, 451 S. |
| ISBN: | 0821845276 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV002757731 | ||
| 003 | DE-604 | ||
| 005 | 20090803 | ||
| 007 | t | ||
| 008 | 900720s1989 xxu |||| 00||| engod | ||
| 020 | |a 0821845276 |9 0-8218-4527-6 | ||
| 035 | |a (OCoLC)467926274 | ||
| 035 | |a (DE-599)BVBBV002757731 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 1 | |a eng |h rus | |
| 044 | |a xxu |c XD-US | ||
| 049 | |a DE-12 |a DE-384 |a DE-355 |a DE-824 |a DE-29T |a DE-91G |a DE-92 |a DE-19 |a DE-521 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA404.5.K3413 1989 | |
| 082 | 1 | |a 515.243 3 |2 22 | |
| 082 | 0 | |a 515/.2433 19 | |
| 084 | |a SK 470 |0 (DE-625)143241: |2 rvk | ||
| 084 | |a MAT 302f |2 stub | ||
| 084 | |a MAT 338f |2 stub | ||
| 100 | 1 | |a Kašin, Boris S. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Ortogonal'nye rjady |
| 245 | 1 | 0 | |a Orthogonal series |c B. S. Kashin ; A. A. Saakyan |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 1989 | |
| 300 | |a XII, 451 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 75 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Approximation | |
| 650 | 4 | |a Développement série orthogonale | |
| 650 | 4 | |a Système FABER-SCHAUDER | |
| 650 | 4 | |a Système FRANKLIN | |
| 650 | 4 | |a Système HAAR | |
| 650 | 4 | |a Système WALSH | |
| 650 | 7 | |a Séries orthogonales |2 ram | |
| 650 | 4 | |a Transformation HILBERT | |
| 650 | 4 | |a Series, Orthogonal | |
| 650 | 0 | 7 | |a Orthogonalentwicklung |0 (DE-588)4172867-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Orthogonalentwicklung |0 (DE-588)4172867-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Saakjan, Artur A. |e Verfasser |4 aut | |
| 830 | 0 | |a Translations of mathematical monographs |v 75 |w (DE-604)BV000002394 |9 75 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001762869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001762869 | ||
Datensatz im Suchindex
| _version_ | 1804117110448717824 |
|---|---|
| adam_text | Contents
Preface ix
Summary of Notation xi
CHAPTER I. Introductory Concepts and Some General Results 1
§ 1. Types of convergence 1
§2. Completeness, totality, biorthogonality 5
§3. Fourier coefficients and partial sums of an orthogonal series 7
§4. The basis property 9
CHAPTER II. Independent Functions and Their First Applications 17
§ 1. Definition and construction of sequences of independent
functions 17
§2. Properties of systems of independent functions 24
§3. Convergence for almost all choices of signs, and
unconditional convergence 38
§4. Random permutations 51
CHAPTER III. The Haar System 61
§ 1. Definition; form of the partial sums 61
§2. Inequalities for coefficients and theorems on the convergence
of Fourier Haar series 64
§3. Unconditional convergence of Fourier Haar series
in Z/(0,1) 71
§4. Convergence almost everywhere and in measure of Fourier
series in the Haar system 87
§5. Absolute convergence almost everywhere and unconditional
convergence almost everywhere for Haar series 93
§6. Transformations of the Haar system 100
V
vi CONTENTS
CHAPTER IV. Some Results on the Trigonometric and Walsh
Systems 105
§ 1. Properties of the partial sums of Fourier series, Fourier
coefficients, and Fejer means 105
§2. Best approximation. Vallee Poussin means 110
§3. Convergence of trigonometric series in LP and almost
everywhere 114
§4. Uniform and absolute convergence of Fourier series 122
§5. The Walsh system. Definition and some properties 134
CHAPTER V. The Hilbert Transform and some Function Spaces 145
§ 1. The Hilbert transform 145
§2. The spaces Rc/F1 and BMO 160
§3. The spaces ^*(A) and BMO(A) (nonperiodic case) 172
CHAPTER VI. The Faber Schauder and Franklin Systems 185
§ 1. The Faber Schauder system 185
§2. Systems of Faber Schauder type 195
§3. The Franklin system. Definition, elementary properties 197
§4. The exponential inequality for the Franklin functions 201
§5. Unconditional convergence of Fourier Franklin series in the
spaces ;F(A) and IS (0,1) 206
CHAPTER VII. Orthogonalization and Factorization Theorems 221
§ 1. Orthogonalization of a system of functions by means of
extension to a larger set 222
§2. Two theorems on sequences of functions 232
§3. Structure of systems with convergence in measure for I2 241
§4. Properties of the majorant operator for the partial sums 244
CHAPTER VIII. Theorems on the Convergence of General
Orthogonal Series 251
§1. Convergence of orthogonal series almost everywhere 251
§2. Unconditional convergence almost everywhere 265
§3. Subsequences with convergence almost everywhere 272
§4. Lacunary systems 277
§5. Properties of integrated orthonormal systems 288
CONTENTS vii
CHAPTER IX. General Theorems on the Divergence of Orthogonal
Series 293
§ 1. Divergence almost everywhere of rearrangements of L2
Fourier series 293
§2. Fourier coefficients of continuous functions 301
§3. Some properties of uniformly bounded orthonormal systems 311
CHAPTER X. Some Theorems on the Representation of Functions
by Orthogonal Series 341
§1. Representation of functions by series that converge in
measure 342
§2. Representation of functions by series that converge almost
everywhere 350
§3. Two theorems on universal series 373
Appendix 1 385
Appendix 2 401
Notes 421
Bibliography 435
Index 449
|
| any_adam_object | 1 |
| author | Kašin, Boris S. Saakjan, Artur A. |
| author_facet | Kašin, Boris S. Saakjan, Artur A. |
| author_role | aut aut |
| author_sort | Kašin, Boris S. |
| author_variant | b s k bs bsk a a s aa aas |
| building | Verbundindex |
| bvnumber | BV002757731 |
| callnumber-first | Q - Science |
| callnumber-label | QA404 |
| callnumber-raw | QA404.5.K3413 1989 |
| callnumber-search | QA404.5.K3413 1989 |
| callnumber-sort | QA 3404.5 K3413 41989 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 470 |
| classification_tum | MAT 302f MAT 338f |
| ctrlnum | (OCoLC)467926274 (DE-599)BVBBV002757731 |
| dewey-full | 515.2433 515/.243319 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.243 3 515/.2433 19 |
| dewey-search | 515.243 3 515/.2433 19 |
| dewey-sort | 3515.243 13 |
| 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>02040nam a2200565 cb4500</leader><controlfield tag="001">BV002757731</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090803 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">900720s1989 xxu |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821845276</subfield><subfield code="9">0-8218-4527-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)467926274</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002757731</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</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">XD-US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA404.5.K3413 1989</subfield></datafield><datafield tag="082" ind1="1" ind2=" "><subfield code="a">515.243 3</subfield><subfield code="2">22</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.2433 19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 470</subfield><subfield code="0">(DE-625)143241:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 302f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 338f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kašin, Boris S.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Ortogonal'nye rjady</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Orthogonal series</subfield><subfield code="c">B. S. Kashin ; A. A. Saakyan</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, R.I.</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 451 S.</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">75</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus d. Russ. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Approximation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Développement série orthogonale</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Système FABER-SCHAUDER</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Système FRANKLIN</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Système HAAR</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Système WALSH</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Séries orthogonales</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transformation HILBERT</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Series, Orthogonal</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Orthogonalentwicklung</subfield><subfield code="0">(DE-588)4172867-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Orthogonalentwicklung</subfield><subfield code="0">(DE-588)4172867-1</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">Saakjan, Artur A.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Translations of mathematical monographs</subfield><subfield code="v">75</subfield><subfield code="w">(DE-604)BV000002394</subfield><subfield code="9">75</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=001762869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="n">oe</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001762869</subfield></datafield></record></collection> |
| id | DE-604.BV002757731 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:49:11Z |
| institution | BVB |
| isbn | 0821845276 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001762869 |
| oclc_num | 467926274 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-355 DE-BY-UBR DE-824 DE-29T DE-91G DE-BY-TUM DE-92 DE-19 DE-BY-UBM DE-521 DE-83 DE-188 |
| owner_facet | DE-12 DE-384 DE-355 DE-BY-UBR DE-824 DE-29T DE-91G DE-BY-TUM DE-92 DE-19 DE-BY-UBM DE-521 DE-83 DE-188 |
| physical | XII, 451 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Kašin, Boris S. Verfasser aut Ortogonal'nye rjady Orthogonal series B. S. Kashin ; A. A. Saakyan Providence, R.I. American Mathematical Society 1989 XII, 451 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 75 Aus d. Russ. übers. Approximation Développement série orthogonale Système FABER-SCHAUDER Système FRANKLIN Système HAAR Système WALSH Séries orthogonales ram Transformation HILBERT Series, Orthogonal Orthogonalentwicklung (DE-588)4172867-1 gnd rswk-swf Orthogonalentwicklung (DE-588)4172867-1 s DE-604 Saakjan, Artur A. Verfasser aut Translations of mathematical monographs 75 (DE-604)BV000002394 75 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001762869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kašin, Boris S. Saakjan, Artur A. Orthogonal series Translations of mathematical monographs Approximation Développement série orthogonale Système FABER-SCHAUDER Système FRANKLIN Système HAAR Système WALSH Séries orthogonales ram Transformation HILBERT Series, Orthogonal Orthogonalentwicklung (DE-588)4172867-1 gnd |
| subject_GND | (DE-588)4172867-1 |
| title | Orthogonal series |
| title_alt | Ortogonal'nye rjady |
| title_auth | Orthogonal series |
| title_exact_search | Orthogonal series |
| title_full | Orthogonal series B. S. Kashin ; A. A. Saakyan |
| title_fullStr | Orthogonal series B. S. Kashin ; A. A. Saakyan |
| title_full_unstemmed | Orthogonal series B. S. Kashin ; A. A. Saakyan |
| title_short | Orthogonal series |
| title_sort | orthogonal series |
| topic | Approximation Développement série orthogonale Système FABER-SCHAUDER Système FRANKLIN Système HAAR Système WALSH Séries orthogonales ram Transformation HILBERT Series, Orthogonal Orthogonalentwicklung (DE-588)4172867-1 gnd |
| topic_facet | Approximation Développement série orthogonale Système FABER-SCHAUDER Système FRANKLIN Système HAAR Système WALSH Séries orthogonales Transformation HILBERT Series, Orthogonal Orthogonalentwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001762869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT kasinboriss ortogonalnyerjady AT saakjanartura ortogonalnyerjady AT kasinboriss orthogonalseries AT saakjanartura orthogonalseries |