Faber Series for L2 Holomorphic One-Forms on Riemann Surfaces with Boundary
Consider a compact surface R with distinguished points z1,…,zn and conformal maps fk from the unit disk into non-overlapping quasidisks on R taking 0 to zk. Let Σ be the Riemann surface obtained by removing the closures of the images of fk from R. We define forms which are meromorphic on R with pole...
Saved in:
| Published in | Computational methods and function theory Vol. 25; no. 2; pp. 329 - 347 |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Springer Nature B.V
01.06.2025
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1617-9447 2195-3724 |
| DOI | 10.1007/s40315-024-00529-4 |
Cover
Loading…
| Abstract | Consider a compact surface R with distinguished points z1,…,zn and conformal maps fk from the unit disk into non-overlapping quasidisks on R taking 0 to zk. Let Σ be the Riemann surface obtained by removing the closures of the images of fk from R. We define forms which are meromorphic on R with poles only at z1,…,zn, which we call Faber–Tietz forms. These are analogous to Faber polynomials in the sphere. We show that any L2 holomorphic one-form on Σ is uniquely expressible as a series of Faber–Tietz forms. This series converges both in L2(Σ) and uniformly on compact subsets of Σ. |
|---|---|
| AbstractList | Consider a compact surface R with distinguished points z1,…,zn and conformal maps fk from the unit disk into non-overlapping quasidisks on R taking 0 to zk. Let Σ be the Riemann surface obtained by removing the closures of the images of fk from R. We define forms which are meromorphic on R with poles only at z1,…,zn, which we call Faber–Tietz forms. These are analogous to Faber polynomials in the sphere. We show that any L2 holomorphic one-form on Σ is uniquely expressible as a series of Faber–Tietz forms. This series converges both in L2(Σ) and uniformly on compact subsets of Σ. |
| BookMark | eNotjctKAzEYRoNUsK2-gKuA62j-XCaTpRZrxYGC1XXJlU5pk5p0EN_eAV19m3PON0OTlFNA6BboPVCqHqqgHCShTBBKJdNEXKApAy0JV0xM0BQaUEQLoa7QrNb9CAnN-RS9LY0NBW9C6UPFMRfcMbzKh3zM5bTrHV6nQJa5HCvOCb_34WhSwpuhRONG4bs_7_BTHpI35ecaXUZzqOHmf-foc_n8sViRbv3yunjsyAlafiaNYM4yS23rtdA-RmCRWy88UC9BRRGU07z10oG0lkblnbWWGddwT0EyPkd3f91TyV9DqOftPg8ljZdbzmgjpYa25b-8zFFQ |
| ContentType | Journal Article |
| Copyright | Copyright Springer Nature B.V. 2025 |
| Copyright_xml | – notice: Copyright Springer Nature B.V. 2025 |
| DOI | 10.1007/s40315-024-00529-4 |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2195-3724 |
| EndPage | 347 |
| GroupedDBID | 06D 0R~ 199 203 2LR 30V 4.4 406 95. 96X AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAZMS ABAKF ABBRH ABDBE ABDZT ABECU ABFSG ABFTV ABJNI ABJOX ABKCH ABMQK ABQBU ABRTQ ABTEG ABTHY ABTKH ABTMW ABXPI ACAOD ACCUX ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMLO ACOKC ACPIV ACSTC ACZOJ ADHHG ADHIR ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETCA AEVLU AEXYK AEZWR AFBBN AFDZB AFHIU AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGMZJ AGQEE AGQMX AGRTI AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHWEU AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJRNO AJZVZ AKLTO ALMA_UNASSIGNED_HOLDINGS AM4 AMKLP AMXSW AMYLF AMYQR ANMIH ARMRJ ASPBG ATHPR AUKKA AVWKF AXYYD AYFIA AYJHY BAPOH BGNMA CSCUP DNIVK DPUIP EBLON EBS EIOEI ESBYG FERAY FIGPU FNLPD FRRFC FYJPI GGCAI GGRSB GJIRD HMJXF HRMNR IKXTQ IWAJR IXD J-C J9A JBSCW JZLTJ KOV L7B LLZTM M4Y NPVJJ NQJWS NU0 O93 O9G O9J PT4 ROL RSV SHX SISQX SJN SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE TR2 TSG UG4 UOJIU UTJUX UZXMN VFIZW W48 ZMTXR |
| ID | FETCH-LOGICAL-p183t-642cb2b0b8d949dff12f3bd4d10d517f4e7c938d5c15bb0f7dcbbb2ac63d01523 |
| ISSN | 1617-9447 |
| IngestDate | Sun Jul 13 05:06:48 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-p183t-642cb2b0b8d949dff12f3bd4d10d517f4e7c938d5c15bb0f7dcbbb2ac63d01523 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 3206559188 |
| PQPubID | 2043941 |
| PageCount | 19 |
| ParticipantIDs | proquest_journals_3206559188 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-06-01 |
| PublicationDateYYYYMMDD | 2025-06-01 |
| PublicationDate_xml | – month: 06 year: 2025 text: 2025-06-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Heidelberg |
| PublicationPlace_xml | – name: Heidelberg |
| PublicationTitle | Computational methods and function theory |
| PublicationYear | 2025 |
| Publisher | Springer Nature B.V |
| Publisher_xml | – name: Springer Nature B.V |
| SSID | ssj0054933 |
| Score | 2.3200262 |
| Snippet | Consider a compact surface R with distinguished points z1,…,zn and conformal maps fk from the unit disk into non-overlapping quasidisks on R taking 0 to zk.... |
| SourceID | proquest |
| SourceType | Aggregation Database |
| StartPage | 329 |
| SubjectTerms | Conformal mapping Polynomials Riemann surfaces |
| Title | Faber Series for L2 Holomorphic One-Forms on Riemann Surfaces with Boundary |
| URI | https://www.proquest.com/docview/3206559188 |
| Volume | 25 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3Na9swFBdtetkOY1tX9tEVHXYrKrEkf-jYjJrQpSmUBHILfpINPdQZiXvpX9-nL7chZXS9CCODbPST3pfeT4-QX7aMdlUA7jSVCiYr0Ew1RjHcSspmWqQSLBv5apqN5_JykS5ihezALungTD-8yCt5C6rYh7halux_INsPih34jPhiiwhj-yqMywrqtd3u6O66fMEJPx2jNLtb4ezd6tPrtmYlGqXuSODmtr6rWtzN9-vG5WG5EOzIlVXa5kX7Sg8xSuhrTPurnK0WdAumi5T-PmTA06fUpq2Qoc2HtqcUPaXFSUA0aZiS_hrMs9r1cVvQUeSe7BzFpucrh-XBn8lAEUIYXp0KP9KOpPbJGRtpq0wwNBSYO3MMjJ-ta7Gn18tyPpksZxeL2T454OgP8AE5OC9Ho2lUuujlCseliH8f-FGOJbnzjR2964yJ2UfyIXgB9NxD-ons1e1n8v6qv0J3c0j-OHCpB5ciuHTC6TNwaQ8uXbU0gEsjuNSCSyO4X8i8vJj9HrNQ-YL9RRHbMXQKNXAYQmGUVKZpEt4IMNIkQ5MmeSPrXCtRmFQnKcCwyY0GAF7pTBi077g4IoN21dZfCZUgKrBknSzLcZKqIisynaOGFlBBooffyHGci2VY2pul4GiZpiopiu__fv2DvHtaYMdk0K3v659opXVwEhB6BB6yPYU |
| linkProvider | Library Specific Holdings |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Faber+Series+for+L2+Holomorphic+One-Forms+on+Riemann+Surfaces+with+Boundary&rft.jtitle=Computational+methods+and+function+theory&rft.date=2025-06-01&rft.pub=Springer+Nature+B.V&rft.issn=1617-9447&rft.eissn=2195-3724&rft.volume=25&rft.issue=2&rft.spage=329&rft.epage=347&rft_id=info:doi/10.1007%2Fs40315-024-00529-4&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1617-9447&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1617-9447&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1617-9447&client=summon |