Some Properties of Range Operators on LCA Groups

• Published in: Kragujevac Journal of Mathematics Vol. 47; no. 7; p. 995
• Main Authors: VERMA, RUCHIKA, TEENA, KUMARI
• Format: Journal Article
• Language: English
• Published: 2023
• ISSN: 1450-9628; 2406-3045
• DOI: 10.46793/KgJMat2307.0995V

In this paper, we study the structure of shift preserving operators acting on shift-invariant spaces in L2(G), where G is a locally compact Abelian group. We generalize some results related to shift-preserving operator and its associated range operator from L2(ℝd) to L2(G). We investigate the matrix structure of range operator R(ξ) on range function J associated to shift-invariant space V , in the case of a locally compact Abelian group G. We also focus on some properties like as normal and unitary operator for range operator on L2(G). We show that shift preserving operator U is invertible if and only if fiber of corresponding range operator R is invertible and investigate the measurability of inverse R−1(ξ) of range operator on L2(G).