Generalized analytic continuation:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2002]
|
| Series: | University lecture series
Volume 25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 149 Seiten |
| ISBN: | 0821831755 9780821831755 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV014410870 | ||
| 003 | DE-604 | ||
| 005 | 20230330 | ||
| 007 | t | ||
| 008 | 020603s2002 xxu |||| 00||| eng d | ||
| 010 | |a 2002018463 | ||
| 020 | |a 0821831755 |9 0-8218-3175-5 | ||
| 020 | |a 9780821831755 |9 978-0-8218-3175-5 | ||
| 035 | |a (OCoLC)49283950 | ||
| 035 | |a (DE-599)BVBBV014410870 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-355 |a DE-91G |a DE-739 |a DE-83 |a DE-11 | ||
| 050 | 0 | |a QA331.7 | |
| 082 | 0 | |a 515/.9 |2 21 | |
| 084 | |a SI 165 |0 (DE-625)143085: |2 rvk | ||
| 084 | |a SK 470 |0 (DE-625)143241: |2 rvk | ||
| 084 | |a MAT 302f |2 stub | ||
| 084 | |a 47B38 |2 msc | ||
| 084 | |a 30B40 |2 msc | ||
| 084 | |a 30B30 |2 msc | ||
| 100 | 1 | |a Ross, William T. |d 1964- |e Verfasser |0 (DE-588)173401414 |4 aut | |
| 245 | 1 | 0 | |a Generalized analytic continuation |c William T. Ross ; Harold S. Shapiro |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2002] | |
| 264 | 4 | |c © 2002 | |
| 300 | |a xiii, 149 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a University lecture series |v Volume 25 | |
| 650 | 7 | |a Analytische functies |2 gtt | |
| 650 | 4 | |a Prolongement analytique | |
| 650 | 4 | |a Analytic continuation | |
| 650 | 0 | 7 | |a Analytische Fortsetzung |0 (DE-588)4142347-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Analytische Fortsetzung |0 (DE-588)4142347-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Shapiro, Harold S. |d 1928-2021 |e Verfasser |0 (DE-588)130422924 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-2172-4 |
| 830 | 0 | |a University lecture series |v Volume 25 |w (DE-604)BV004153846 |9 25 | |
| 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=009856303&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009856303 | ||
Record in the Search Index
| _version_ | 1804129269189705728 |
|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Overview 1
Chapter 2. Notation and Preliminaries 11
2.1. Sets 11
2.2. Function Spaces 11
Chapter 3. The Poincare example 17
3.1. Poincare s result 17
3.2. Matching non tangential boundary values 18
Chapter 4. Borel s ideas and their later development 21
4.1. Superconvergence 21
4.2. Borel series 25
Chapter 5. Goncar Continuation 37
5.1. Hyperconvergence 37
5.2. Goncar continuation 41
Chapter 6. Pseudocontinuation 45
6.1. A problem of Walsh and Tumarkin 45
6.2. Definition and basic examples 49
6.3. Cyclic vectors for the backward shift on H2 52
6.4. The Hardy space of a multiply connected domain 56
6.5. Walsh Tumarkin again 58
6.6. Other spaces of analytic functions 59
6.7. The Darlington synthesis problem 63
6.8. Linear differential equations of infinite order 65
6.9. Gap theorems 74
6.10. Functional equations and non continuability 83
Chapter 7. A continuation involving almost periodic functions 89
7.1. Revisiting the Poincare example 89
7.2. A primer on almost periodic functions 91
7.3. Compatibility with analytic continuation 93
Chapter 8. Continuation by formal multiplication of series 99
8.1. Definition 100
8.2. Compatibility with analytic continuation 101
8.3. Cyclic vectors for backward shifts 104
8.4. Spectral properties 113
vii
viii CONTENTS
8.5. Uniqueness 121
8.6. A continuation arising from overconvergence 123
8.7. Generalizing the Walsh Tumarkin results 125
8.8. Possible generalizations 128
Chapter 9. Generalized analytic continuation 131
9.1. Axiomatizing the notion of GAC 131
9.2. Compatibility 132
List of Symbols 139
Bibliography 141
Index 147
|
| any_adam_object | 1 |
| author | Ross, William T. 1964- Shapiro, Harold S. 1928-2021 |
| author_GND | (DE-588)173401414 (DE-588)130422924 |
| author_facet | Ross, William T. 1964- Shapiro, Harold S. 1928-2021 |
| author_role | aut aut |
| author_sort | Ross, William T. 1964- |
| author_variant | w t r wt wtr h s s hs hss |
| building | Verbundindex |
| bvnumber | BV014410870 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331.7 |
| callnumber-search | QA331.7 |
| callnumber-sort | QA 3331.7 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 165 SK 470 |
| classification_tum | MAT 302f |
| ctrlnum | (OCoLC)49283950 (DE-599)BVBBV014410870 |
| dewey-full | 515/.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
| dewey-search | 515/.9 |
| dewey-sort | 3515 19 |
| 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>01986nam a2200529 cb4500</leader><controlfield tag="001">BV014410870</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230330 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">020603s2002 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2002018463</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821831755</subfield><subfield code="9">0-8218-3175-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821831755</subfield><subfield code="9">978-0-8218-3175-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)49283950</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014410870</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</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-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA331.7</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.9</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 165</subfield><subfield code="0">(DE-625)143085:</subfield><subfield code="2">rvk</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">47B38</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">30B40</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">30B30</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ross, William T.</subfield><subfield code="d">1964-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)173401414</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Generalized analytic continuation</subfield><subfield code="c">William T. Ross ; Harold S. Shapiro</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, Rhode Island</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">[2002]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiii, 149 Seiten</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">University lecture series</subfield><subfield code="v">Volume 25</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analytische functies</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Prolongement analytique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analytic continuation</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analytische Fortsetzung</subfield><subfield code="0">(DE-588)4142347-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Analytische Fortsetzung</subfield><subfield code="0">(DE-588)4142347-1</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">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="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-2172-4</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">University lecture series</subfield><subfield code="v">Volume 25</subfield><subfield code="w">(DE-604)BV004153846</subfield><subfield code="9">25</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=009856303&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:BVB01-009856303</subfield></datafield></record></collection> |
| id | DE-604.BV014410870 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:02:27Z |
| institution | BVB |
| isbn | 0821831755 9780821831755 |
| language | English |
| lccn | 2002018463 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009856303 |
| oclc_num | 49283950 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-739 DE-83 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-739 DE-83 DE-11 |
| physical | xiii, 149 Seiten |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Ross, William T. 1964- Verfasser (DE-588)173401414 aut Generalized analytic continuation William T. Ross ; Harold S. Shapiro Providence, Rhode Island American Mathematical Society [2002] © 2002 xiii, 149 Seiten txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 25 Analytische functies gtt Prolongement analytique Analytic continuation Analytische Fortsetzung (DE-588)4142347-1 gnd rswk-swf Analytische Fortsetzung (DE-588)4142347-1 s DE-604 Shapiro, Harold S. 1928-2021 Verfasser (DE-588)130422924 aut Erscheint auch als Online-Ausgabe 978-1-4704-2172-4 University lecture series Volume 25 (DE-604)BV004153846 25 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009856303&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ross, William T. 1964- Shapiro, Harold S. 1928-2021 Generalized analytic continuation University lecture series Analytische functies gtt Prolongement analytique Analytic continuation Analytische Fortsetzung (DE-588)4142347-1 gnd |
| subject_GND | (DE-588)4142347-1 |
| title | Generalized analytic continuation |
| title_auth | Generalized analytic continuation |
| title_exact_search | Generalized analytic continuation |
| title_full | Generalized analytic continuation William T. Ross ; Harold S. Shapiro |
| title_fullStr | Generalized analytic continuation William T. Ross ; Harold S. Shapiro |
| title_full_unstemmed | Generalized analytic continuation William T. Ross ; Harold S. Shapiro |
| title_short | Generalized analytic continuation |
| title_sort | generalized analytic continuation |
| topic | Analytische functies gtt Prolongement analytique Analytic continuation Analytische Fortsetzung (DE-588)4142347-1 gnd |
| topic_facet | Analytische functies Prolongement analytique Analytic continuation Analytische Fortsetzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009856303&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
| work_keys_str_mv | AT rosswilliamt generalizedanalyticcontinuation AT shapiroharolds generalizedanalyticcontinuation |