Smoothing and approximation of functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
van Nostrand
1969
|
| Schriftenreihe: | Van Nostrand Reinhold mathematical studies
24 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 134 S. |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV001937054 | ||
| 003 | DE-604 | ||
| 005 | 20100714 | ||
| 007 | t | ||
| 008 | 890928s1969 |||| 00||| eng d | ||
| 035 | |a (OCoLC)60297 | ||
| 035 | |a (DE-599)BVBBV001937054 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-355 |a DE-824 |a DE-29T |a DE-20 |a DE-19 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA221 | |
| 082 | 0 | |a 517/.5 |2 18 | |
| 084 | |a SK 470 |0 (DE-625)143241: |2 rvk | ||
| 084 | |a 41-01 |2 msc | ||
| 100 | 1 | |a Shapiro, Harold S. |d 1928-2021 |e Verfasser |0 (DE-588)130422924 |4 aut | |
| 245 | 1 | 0 | |a Smoothing and approximation of functions |c by Harold S. Shapiro |
| 264 | 1 | |a New York |b van Nostrand |c 1969 | |
| 300 | |a VIII, 134 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Van Nostrand Reinhold mathematical studies |v 24 | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Functions | |
| 650 | 0 | 7 | |a Approximationstheorie |0 (DE-588)4120913-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |D s |
| 689 | 0 | 1 | |a Approximation |0 (DE-588)4002498-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Approximationstheorie |0 (DE-588)4120913-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Van Nostrand Reinhold mathematical studies |v 24 |w (DE-604)BV002492122 |9 24 | |
| 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=001262520&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001262520 | ||
Datensatz im Suchindex
| _version_ | 1804116377051594752 |
|---|---|
| adam_text | CONTENTS
Preface Hi
Chapter I. Introduction 1
§1.1 What is approximation theory? 1
§1.2 An Example 3
§1.3 Convolutions 6
§1.4 Convolutions, cont d 8
Chapter II. Some Elementary Theorems on Approximation... 11
§2.1 Some applications of convolutions to approximation. 11
§2.2 A theorem on pointwise convergence 14
§2.3 Degree of approximation 21
Chapter III. Some Saturation Theorems 23
§3.1 An Example 23
§3.2 Saturation theorems, regular kinds; mollifiers.... 26
§3.3 Saturation theorems, regular kernels 32
§3.4 Application of harmonic analysis 36
§3.5 Digression; further applications of mollifiers 38
3.5.1 Another method of regularization 42
Chapter IV. Direct Theorems, Degree of Approximation 47
§4.1 Introduction 47
§4.2 Fundamental direct theorem—first variant 51
§4.3 Fundamental direct theorem—second variant 54
§4.4 Fundamental idrect theorem—third variant 58
4.4.1 Use of 2n integrating kernel 58
4.4.2 Best possible constants 62
4.4.3 Approximation of classes of functions 63
vii
vl SMOOTHING AND APPROXIMATION OF FUNCTIONS
§4.5 Localization theorem 54
Chapter V. Inverse Theorems. ...; 67
§5.1 Orientation, classical theory 67
§5.2 Comparison theorems 75
5.2.1 Fourier Stieltjes transforms 77
5.2.2 A comparison theorem based on global
divisibility 78
5.2.3 A comparison theorem based on local
divisibility 82
§5.3 Applications of the comparison theorems 85
5.3.1 Modulus of smoothness, and differentiability. ... 85
5.3.2 New deduction of Jackson s theorem 88
5.3.3 The moving average, revisited 89
§5.4 Special comparison theorems, no divisibility
hypothesis 90
5.4.1 Relation between moduli of smoothness of
different orders 95
5.4.2 New deviations of Theorems 26 and 27 95
5.4.3 Applications to harmonic functions 96
§5.5 Further remarks on saturation 102
§5.6 A final remark concerning Jackson s Theorem 110
Additional Notes 113
Bibliography 127
|
| any_adam_object | 1 |
| author | Shapiro, Harold S. 1928-2021 |
| author_GND | (DE-588)130422924 |
| author_facet | Shapiro, Harold S. 1928-2021 |
| author_role | aut |
| author_sort | Shapiro, Harold S. 1928-2021 |
| author_variant | h s s hs hss |
| building | Verbundindex |
| bvnumber | BV001937054 |
| callnumber-first | Q - Science |
| callnumber-label | QA221 |
| callnumber-raw | QA221 |
| callnumber-search | QA221 |
| callnumber-sort | QA 3221 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 470 |
| ctrlnum | (OCoLC)60297 (DE-599)BVBBV001937054 |
| dewey-full | 517/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517/.5 |
| dewey-search | 517/.5 |
| dewey-sort | 3517 15 |
| 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>01747nam a2200445 cb4500</leader><controlfield tag="001">BV001937054</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100714 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1969 |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)60297</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV001937054</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="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA221</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">517/.5</subfield><subfield code="2">18</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">41-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Shapiro, Harold S.</subfield><subfield code="d">1928-2021</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)130422924</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Smoothing and approximation of functions</subfield><subfield code="c">by Harold S. Shapiro</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">van Nostrand</subfield><subfield code="c">1969</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 134 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">Van Nostrand Reinhold mathematical studies</subfield><subfield code="v">24</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Approximation theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Approximationstheorie</subfield><subfield code="0">(DE-588)4120913-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktion</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4071510-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Approximation</subfield><subfield code="0">(DE-588)4002498-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktion</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4071510-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Approximation</subfield><subfield code="0">(DE-588)4002498-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Approximationstheorie</subfield><subfield code="0">(DE-588)4120913-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Van Nostrand Reinhold mathematical studies</subfield><subfield code="v">24</subfield><subfield code="w">(DE-604)BV002492122</subfield><subfield code="9">24</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=001262520&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:BVB01-001262520</subfield></datafield></record></collection> |
| id | DE-604.BV001937054 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:37:32Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001262520 |
| oclc_num | 60297 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-83 DE-188 |
| physical | VIII, 134 S. |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | van Nostrand |
| record_format | marc |
| series | Van Nostrand Reinhold mathematical studies |
| series2 | Van Nostrand Reinhold mathematical studies |
| spelling | Shapiro, Harold S. 1928-2021 Verfasser (DE-588)130422924 aut Smoothing and approximation of functions by Harold S. Shapiro New York van Nostrand 1969 VIII, 134 S. txt rdacontent n rdamedia nc rdacarrier Van Nostrand Reinhold mathematical studies 24 Approximation theory Functions Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 s Approximation (DE-588)4002498-2 s DE-604 Approximationstheorie (DE-588)4120913-8 s Van Nostrand Reinhold mathematical studies 24 (DE-604)BV002492122 24 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001262520&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shapiro, Harold S. 1928-2021 Smoothing and approximation of functions Van Nostrand Reinhold mathematical studies Approximation theory Functions Approximationstheorie (DE-588)4120913-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4120913-8 (DE-588)4071510-3 (DE-588)4002498-2 |
| title | Smoothing and approximation of functions |
| title_auth | Smoothing and approximation of functions |
| title_exact_search | Smoothing and approximation of functions |
| title_full | Smoothing and approximation of functions by Harold S. Shapiro |
| title_fullStr | Smoothing and approximation of functions by Harold S. Shapiro |
| title_full_unstemmed | Smoothing and approximation of functions by Harold S. Shapiro |
| title_short | Smoothing and approximation of functions |
| title_sort | smoothing and approximation of functions |
| topic | Approximation theory Functions Approximationstheorie (DE-588)4120913-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Approximation theory Functions Approximationstheorie Funktion Mathematik Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001262520&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002492122 |
| work_keys_str_mv | AT shapiroharolds smoothingandapproximationoffunctions |