Cauchy transformation and mutual dualities between A^{-\infty}(\Omega) and A^\infty(\complement\Omega) for Carathéodory domains
Let \Omega be a Carathéodory domain in the complex plane \mathbb C, A^{-\infty}(\Omega) the space of functions that are holomorphic in \Omega with polynomial growth near the boundary \partial\Omega, and A^\infty(\complement\Omega) the space of holomorphic functions in the interior of \complement\Ome...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Abanin, A.V [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: © Copyright 2016 The Belgian Mathematic Society |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Bulletin of the Belgian Mathematical Society - Simon Stevin - Brussels : Soc., 1994, 23(2016), no. 1, Seite 87-102 |
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volume:23 ; year:2016 ; number:no. 1 ; pages:87-102 |
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| 520 | |a Let \Omega be a Carathéodory domain in the complex plane \mathbb C, A^{-\infty}(\Omega) the space of functions that are holomorphic in \Omega with polynomial growth near the boundary \partial\Omega, and A^\infty(\complement\Omega) the space of holomorphic functions in the interior of \complement\Omega:=\overline{\mathbb C}\setminus\Omega, vanishing at infinity and being in C^\infty(\complement\Omega). We prove that the Cauchy transformation of analytic functionals establishes a mutual duality between spaces A^{-\infty}(\Omega) and A^\infty(\complement\Omega). This result, together with those of [3], gives a solution to duality problem for the space A^{-\infty}(\Omega) in both one and several complex variables. | ||
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Cauchy transformation and mutual dualities between A^{-\infty}(\Omega) and A^\infty(\complement\Omega) for Carathéodory domains |
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Let \Omega be a Carathéodory domain in the complex plane \mathbb C, A^{-\infty}(\Omega) the space of functions that are holomorphic in \Omega with polynomial growth near the boundary \partial\Omega, and A^\infty(\complement\Omega) the space of holomorphic functions in the interior of \complement\Omega:=\overline{\mathbb C}\setminus\Omega, vanishing at infinity and being in C^\infty(\complement\Omega). We prove that the Cauchy transformation of analytic functionals establishes a mutual duality between spaces A^{-\infty}(\Omega) and A^\infty(\complement\Omega). This result, together with those of [3], gives a solution to duality problem for the space A^{-\infty}(\Omega) in both one and several complex variables. |
| abstractGer |
Let \Omega be a Carathéodory domain in the complex plane \mathbb C, A^{-\infty}(\Omega) the space of functions that are holomorphic in \Omega with polynomial growth near the boundary \partial\Omega, and A^\infty(\complement\Omega) the space of holomorphic functions in the interior of \complement\Omega:=\overline{\mathbb C}\setminus\Omega, vanishing at infinity and being in C^\infty(\complement\Omega). We prove that the Cauchy transformation of analytic functionals establishes a mutual duality between spaces A^{-\infty}(\Omega) and A^\infty(\complement\Omega). This result, together with those of [3], gives a solution to duality problem for the space A^{-\infty}(\Omega) in both one and several complex variables. |
| abstract_unstemmed |
Let \Omega be a Carathéodory domain in the complex plane \mathbb C, A^{-\infty}(\Omega) the space of functions that are holomorphic in \Omega with polynomial growth near the boundary \partial\Omega, and A^\infty(\complement\Omega) the space of holomorphic functions in the interior of \complement\Omega:=\overline{\mathbb C}\setminus\Omega, vanishing at infinity and being in C^\infty(\complement\Omega). We prove that the Cauchy transformation of analytic functionals establishes a mutual duality between spaces A^{-\infty}(\Omega) and A^\infty(\complement\Omega). This result, together with those of [3], gives a solution to duality problem for the space A^{-\infty}(\Omega) in both one and several complex variables. |
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| container_issue |
no. 1 |
| title_short |
Cauchy transformation and mutual dualities between A^{-\infty}(\Omega) and A^\infty(\complement\Omega) for Carathéodory domains |
| url |
http://projecteuclid.org/euclid.bbms/1457560856 |
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| author2 |
Khoi, Le Hai |
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| up_date |
2024-07-04T04:00:34.651Z |
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