Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains

• المؤلفون الرئيسيون: Khoi, Le Hai., Ishimura, Ryuichi., Abanin, Alexander V.
• مؤلفون آخرون: School of Physical and Mathematical Sciences
• التنسيق: مقال
• اللغة: English
• منشور في: 2013
• الموضوعات: DRNTU::Science::Mathematics
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/99099; http://hdl.handle.net/10220/12746
• المؤسسة: Nanyang Technological University

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.