A criterion for the explicit reconstruction of a holomorphic function from its restrictions on lines

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:420

Article

关键词: Complex variables;    Approximation theory;    Interpolation theory;    Divided differences;   

DOI  :  10.1016/j.jmaa.2014.06.004

来源: Elsevier

【 摘 要 】

We deal with a problem of the explicit reconstruction of any holomorphic function f on a ball of C-2 from its restrictions on a union of complex lines. The validity of such a reconstruction essentially depends on the mutual repartition of these lines. This criterion can be analytically described and it is also possible to give geometrical sufficient conditions. The motivation of this problem also comes from possible applications in mathematical economics and medical imaging. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free