Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains
Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains
复制标题
凸域多项式增长全纯函数空间中卷积方程解的推广
DOI：
10.1016/j.bulsci.2011.06.002
复制
发表时间：
2012
影响因子：
1.3
通讯作者：
R. Ishimura and Le Hai Khoi
中科院分区：
文献类型：
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作者：
A.V. Abanin;R. Ishimura and Le Hai Khoi
本文考虑由算子定义的齐次卷积方程的解的延拓问题，所述齐次卷积方程由算子从D+K边界附近具有多项式增长的全纯函数空间A−∞(D+K)扩展到A−∞(D)型空间(D和K分别是C中的有界凸区域和凸紧集).我们证明了在一定的条件下，每个解都可以推广为A−∞(Ω+K)-解，其中Ω⊃D是一个凸域。
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) of holomorphic functions with polynomial growth near the boundary of D+K into another space of such a type A−∞(D) (D and K being a bounded convex domain and a convex compact set in C, respectively). We show that under some exact conditions each such solution can be extended as A−∞(Ω+K)-solution, where Ω⊃D is a certain convex domain.