Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains
In this paper we consider a problem of extension of solutions to homogeneous convolution equations defined by operators acting from a space A−∞(D+K)A−∞(D+K) of holomorphic functions with polynomial growth near the boundary of D+KD+K into another space of such a type A−∞(D)A−∞(D) (D and K being a bou...
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sg-ntu-dr.10356-990992020-03-07T12:34:48Z Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains Khoi, Le Hai. Ishimura, Ryuichi. Abanin, Alexander V. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics In this paper we consider a problem of extension of solutions to homogeneous convolution equations defined by operators acting from a space A−∞(D+K)A−∞(D+K) of holomorphic functions with polynomial growth near the boundary of D+KD+K into another space of such a type A−∞(D)A−∞(D) (D and K being a bounded convex domain and a convex compact set in CC, respectively). We show that under some exact conditions each such solution can be extended as A−∞(Ω+K)A−∞(Ω+K)-solution, where Ω⊃DΩ⊃D is a certain convex domain. 2013-08-01T03:37:19Z 2019-12-06T20:03:22Z 2013-08-01T03:37:19Z 2019-12-06T20:03:22Z 2011 2011 Journal Article Abanin, A. V., Ishimura, R., & Khoi, L. H. (2012). Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains. Bulletin des sciences mathématiques, 136(1), 96-110. 0007-4497 https://hdl.handle.net/10356/99099 http://hdl.handle.net/10220/12746 10.1016/j.bulsci.2011.06.002 en Bulletin des sciences mathématiques |
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DRNTU::Science::Mathematics Khoi, Le Hai. Ishimura, Ryuichi. Abanin, Alexander V. Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains |
| description |
In this paper we consider a problem of extension of solutions to homogeneous convolution equations defined by operators acting from a space A−∞(D+K)A−∞(D+K) of holomorphic functions with polynomial growth near the boundary of D+KD+K into another space of such a type A−∞(D)A−∞(D) (D and K being a bounded convex domain and a convex compact set in CC, respectively). We show that under some exact conditions each such solution can be extended as A−∞(Ω+K)A−∞(Ω+K)-solution, where Ω⊃DΩ⊃D is a certain convex domain. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Khoi, Le Hai. Ishimura, Ryuichi. Abanin, Alexander V. |
| format |
Article |
| author |
Khoi, Le Hai. Ishimura, Ryuichi. Abanin, Alexander V. |
| author_sort |
Khoi, Le Hai. |
| title |
Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains |
| title_short |
Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains |
| title_full |
Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains |
| title_fullStr |
Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains |
| title_full_unstemmed |
Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains |
| title_sort |
extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains |
| publishDate |
2013 |
| url |
https://hdl.handle.net/10356/99099 http://hdl.handle.net/10220/12746 |
| _version_ |
1681049403668824064 |