On the construction of entire and meromorphic functions of several variables having specified growth, and some applications
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| Titel: | On the construction of entire and meromorphic functions of several variables having specified growth, and some applications |
|---|---|
| Autoren: | Sekerin, A. B. |
| Verlagsinformationen: | American Mathematical Society (AMS), Providence, RI |
| Schlagwörter: | representation of analytic functions in several variables by exponential series, meromorphic function, Special classes of entire functions of one complex variable and growth estimates, Other generalizations of function theory of one complex variable, Meromorphic functions of one complex variable (general theory), approximation, Harmonic, subharmonic, superharmonic functions in higher dimensions, subharmonic functions |
| Beschreibung: | The author generalizes a result concerning the approximation of differences of certain subharmonic functions in \(\mathbb{C} = \mathbb{R}^2\) by the logarithm of the modulus of a meromorphic function to the higher dimensional case. The main result is: Let \(u\) be the difference of subharmonic functions in \(\mathbb{C}^n\) such that \[ |u(z) |\leq c (\varepsilon) |z |^{\rho + \varepsilon} \] \(0 < \rho < 2\), for any \(\varepsilon > 0\) outside a countable union of balls with finite sum of radii, then there are entire functions \(L_1\), \(L_2\) such that outside a \(C_0\)-set \[ \bigl |u(z) - \ln |L_1 (z)/L_2 (z) |\bigr |\leq C \bigl( \ln |z |\bigr)^3 |z |^{\rho (1 - 1/2n}). \] This result is applied to the representation of analytic functions in several variables by exponential series. |
| Publikationsart: | Article |
| Dateibeschreibung: | application/xml |
| Zugangs-URL: | https://zbmath.org/738900 |
| Dokumentencode: | edsair.c2b0b933574d..2a09b0ef0e9dce7e2c3c2c88e39b2bbe |
| Datenbank: | OpenAIRE |
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| Items | – Name: Title Label: Title Group: Ti Data: On the construction of entire and meromorphic functions of several variables having specified growth, and some applications – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Sekerin%2C+A%2E+B%2E%22">Sekerin, A. B.</searchLink> – Name: Publisher Label: Publisher Information Group: PubInfo Data: American Mathematical Society (AMS), Providence, RI – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22representation+of+analytic+functions+in+several+variables+by+exponential+series%22">representation of analytic functions in several variables by exponential series</searchLink><br /><searchLink fieldCode="DE" term="%22meromorphic+function%22">meromorphic function</searchLink><br /><searchLink fieldCode="DE" term="%22Special+classes+of+entire+functions+of+one+complex+variable+and+growth+estimates%22">Special classes of entire functions of one complex variable and growth estimates</searchLink><br /><searchLink fieldCode="DE" term="%22Other+generalizations+of+function+theory+of+one+complex+variable%22">Other generalizations of function theory of one complex variable</searchLink><br /><searchLink fieldCode="DE" term="%22Meromorphic+functions+of+one+complex+variable+%28general+theory%29%22">Meromorphic functions of one complex variable (general theory)</searchLink><br /><searchLink fieldCode="DE" term="%22approximation%22">approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic%2C+subharmonic%2C+superharmonic+functions+in+higher+dimensions%22">Harmonic, subharmonic, superharmonic functions in higher dimensions</searchLink><br /><searchLink fieldCode="DE" term="%22subharmonic+functions%22">subharmonic functions</searchLink> – Name: Abstract Label: Description Group: Ab Data: The author generalizes a result concerning the approximation of differences of certain subharmonic functions in \(\mathbb{C} = \mathbb{R}^2\) by the logarithm of the modulus of a meromorphic function to the higher dimensional case. The main result is: Let \(u\) be the difference of subharmonic functions in \(\mathbb{C}^n\) such that \[ |u(z) |\leq c (\varepsilon) |z |^{\rho + \varepsilon} \] \(0 < \rho < 2\), for any \(\varepsilon > 0\) outside a countable union of balls with finite sum of radii, then there are entire functions \(L_1\), \(L_2\) such that outside a \(C_0\)-set \[ \bigl |u(z) - \ln |L_1 (z)/L_2 (z) |\bigr |\leq C \bigl( \ln |z |\bigr)^3 |z |^{\rho (1 - 1/2n}). \] This result is applied to the representation of analytic functions in several variables by exponential series. – Name: TypeDocument Label: Document Type Group: TypDoc Data: Article – Name: Format Label: File Description Group: SrcInfo Data: application/xml – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="https://zbmath.org/738900" linkWindow="_blank">https://zbmath.org/738900</link> – Name: AN Label: Accession Number Group: ID Data: edsair.c2b0b933574d..2a09b0ef0e9dce7e2c3c2c88e39b2bbe |
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| RecordInfo | BibRecord: BibEntity: Languages: – Text: Undetermined Subjects: – SubjectFull: representation of analytic functions in several variables by exponential series Type: general – SubjectFull: meromorphic function Type: general – SubjectFull: Special classes of entire functions of one complex variable and growth estimates Type: general – SubjectFull: Other generalizations of function theory of one complex variable Type: general – SubjectFull: Meromorphic functions of one complex variable (general theory) Type: general – SubjectFull: approximation Type: general – SubjectFull: Harmonic, subharmonic, superharmonic functions in higher dimensions Type: general – SubjectFull: subharmonic functions Type: general Titles: – TitleFull: On the construction of entire and meromorphic functions of several variables having specified growth, and some applications Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Sekerin, A. B. IsPartOfRelationships: – BibEntity: Identifiers: – Type: issn-locals Value: edsair |
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