Generalized inverses and sampling problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:398

Article

Laura Arias, M.²  Conde, Cristian^1,2 

[1] Univ Nacl Gen Sarmiento, Inst Ciencias, RA-1613 Los Polvorines, Argentina

[2] Consejo Nacl Invest Cient & Tecn, Inst Argentina Matemat Alberto P Calderon, RA-1083 Buenos Aires, DF, Argentina

关键词: Sampling problems;    Consistent reconstructions;    Generalized inverses;   

DOI  :  10.1016/j.jmaa.2012.09.017

来源: Elsevier

【 摘 要 】

Sampling theory is concerned with the problem of reconstructing a signal f in a Hilbert space from a given a collection of sampled values off. If a certain decomposition of the Hilbert space is possible (in terms of the sampling and reconstruction subspaces) then a consistent reconstruction can be obtained. In this paper we treat the case in which such a decomposition cannot be found. For this situation, we study the quasi-consistent reconstructions which are an extension of the consistent reconstructions. We relate the previous concepts to generalized inverses. We also present some new results and problems regarding consistent sampling. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free