Academic Journal
Compactness of the canonical solution operator of \(\bar\partial\) on bounded pseudoconvex domains
| Τίτλος: | Compactness of the canonical solution operator of \(\bar\partial\) on bounded pseudoconvex domains |
|---|---|
| Συγγραφείς: | Knirsch, Wolfgang |
| Στοιχεία εκδότη: | Wiley (Wiley-VCH), Weinheim |
| Θεματικοί όροι: | Bergman spaces of functions in several complex variables, Toeplitz operators, Hankel operators, Wiener-Hopf operators, d-bar equation, Bergman-Toeplitz operators, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, \(\overline\partial\)-Neumann operator, canonical solution operator, \((0,q)\)-forms with holomorphic coefficients |
| Περιγραφή: | The main result of this paper is an explicit formula for the canonical solution operator \(S_{q+1}\) to \(\overline{\partial} \) restricted to \((0,q)\)-forms with holomorphic coefficients. The restriction to forms with holomorphic coefficients is essential for the proof and it shows an interesting relationship of \(\overline{\partial} \) to the Bergman kernel and certain multiplication operators. In the second part the explicit formula for the solution operator to \(\overline{\partial} \) is applied to generalize a result of \textit{N. Salinas}, \textit{A. Sheu} and \textit{H. Upmeier} [Ann. Math. (2) 130, 531--565 (1989; Zbl 0708.47021)], concerning compactness of the solution operator, the \(\overline{\partial} \)- Neumann operator and certain Bergman-Toeplitz operators. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| DOI: | 10.1002/1522-2616(200211)245:1<94::aid-mana94>3.0.co;2-h |
| Σύνδεσμος πρόσβασης: | https://zbmath.org/1848362 |
| Αριθμός Καταχώρησης: | edsair.c2b0b933574d..6d21c153c354d2d2581a48dc12bcc20e |
| Βάση Δεδομένων: | OpenAIRE |
| FullText | Text: Availability: 0 |
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| Header | DbId: edsair DbLabel: OpenAIRE An: edsair.c2b0b933574d..6d21c153c354d2d2581a48dc12bcc20e RelevancyScore: 685 AccessLevel: 3 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 685 |
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| Items | – Name: Title Label: Title Group: Ti Data: Compactness of the canonical solution operator of \(\bar\partial\) on bounded pseudoconvex domains – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Knirsch%2C+Wolfgang%22">Knirsch, Wolfgang</searchLink> – Name: Publisher Label: Publisher Information Group: PubInfo Data: Wiley (Wiley-VCH), Weinheim – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Bergman+spaces+of+functions+in+several+complex+variables%22">Bergman spaces of functions in several complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Toeplitz+operators%2C+Hankel+operators%2C+Wiener-Hopf+operators%22">Toeplitz operators, Hankel operators, Wiener-Hopf operators</searchLink><br /><searchLink fieldCode="DE" term="%22d-bar+equation%22">d-bar equation</searchLink><br /><searchLink fieldCode="DE" term="%22Bergman-Toeplitz+operators%22">Bergman-Toeplitz operators</searchLink><br /><searchLink fieldCode="DE" term="%22%5C%28%5Coverline%5Cpartial%5C%29+and+%5C%28%5Coverline%5Cpartial%5C%29-Neumann+operators%22">\(\overline\partial\) and \(\overline\partial\)-Neumann operators</searchLink><br /><searchLink fieldCode="DE" term="%22%5C%28%5Coverline%5Cpartial%5C%29-Neumann+operator%22">\(\overline\partial\)-Neumann operator</searchLink><br /><searchLink fieldCode="DE" term="%22canonical+solution+operator%22">canonical solution operator</searchLink><br /><searchLink fieldCode="DE" term="%22%5C%28%280%2Cq%29%5C%29-forms+with+holomorphic+coefficients%22">\((0,q)\)-forms with holomorphic coefficients</searchLink> – Name: Abstract Label: Description Group: Ab Data: The main result of this paper is an explicit formula for the canonical solution operator \(S_{q+1}\) to \(\overline{\partial} \) restricted to \((0,q)\)-forms with holomorphic coefficients. The restriction to forms with holomorphic coefficients is essential for the proof and it shows an interesting relationship of \(\overline{\partial} \) to the Bergman kernel and certain multiplication operators. In the second part the explicit formula for the solution operator to \(\overline{\partial} \) is applied to generalize a result of \textit{N. Salinas}, \textit{A. Sheu} and \textit{H. Upmeier} [Ann. Math. (2) 130, 531--565 (1989; Zbl 0708.47021)], concerning compactness of the solution operator, the \(\overline{\partial} \)- Neumann operator and certain Bergman-Toeplitz operators. – Name: TypeDocument Label: Document Type Group: TypDoc Data: Article – Name: Format Label: File Description Group: SrcInfo Data: application/xml – Name: DOI Label: DOI Group: ID Data: 10.1002/1522-2616(200211)245:1<94::aid-mana94>3.0.co;2-h – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="https://zbmath.org/1848362" linkWindow="_blank">https://zbmath.org/1848362</link> – Name: AN Label: Accession Number Group: ID Data: edsair.c2b0b933574d..6d21c153c354d2d2581a48dc12bcc20e |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/1522-2616(200211)245:1<94::aid-mana94>3.0.co;2-h Languages: – Text: Undetermined Subjects: – SubjectFull: Bergman spaces of functions in several complex variables Type: general – SubjectFull: Toeplitz operators, Hankel operators, Wiener-Hopf operators Type: general – SubjectFull: d-bar equation Type: general – SubjectFull: Bergman-Toeplitz operators Type: general – SubjectFull: \(\overline\partial\) and \(\overline\partial\)-Neumann operators Type: general – SubjectFull: \(\overline\partial\)-Neumann operator Type: general – SubjectFull: canonical solution operator Type: general – SubjectFull: \((0,q)\)-forms with holomorphic coefficients Type: general Titles: – TitleFull: Compactness of the canonical solution operator of \(\bar\partial\) on bounded pseudoconvex domains Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Knirsch, Wolfgang IsPartOfRelationships: – BibEntity: Identifiers: – Type: issn-locals Value: edsair |
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