On reconstruction from discrete local moving averages on locally compact abelian groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Devaraj, P.¹ 

[1] Indian Inst Sci Educ & Res Thiruvananthapuram, Sch Math, Thiruvananthapuram, Kerala, India

关键词: Reconstruction;    Deconvolution;    Moving averages;    Difference equations;   

DOI  :  10.1016/j.jmaa.2018.04.052

来源: Elsevier

【 摘 要 】

Let G be a locally compact abelian group and mu be a compactly supported discrete measure on G. We analyse the range of the operator C-mu : C(G) -> C(G) defined by C-mu(f)(x) = (f*mu)(x) = J(G) f (x - y)d mu(y). It is shown that this operator is onto when C is a compactly generated locally compact abelian group and mu satisfies certain compatibility conditions. Furthermore, if C is a compactly generated torsion free locally compact abelian group then the convolution operator is always onto for every non zero compactly supported discrete measure mu. For a g is an element of C(G), we construct a function f is an element of C(G) such that f * mu = g. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free