Pseudoframe multiresolution structure on abelian locally compact groups

Document Type : Research Paper


1 Ph. D. student in Ferdowsi University of Mashhad

2 Department of pure Mathematics; Ferdowsi University of Mashhad;

3 Department of pure Mathematics;Ferdowsi University of Mashhad;


‎Let $G$ be a locally compact abelian group‎. ‎The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$‎. ‎Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level‎. ‎Also‎, ‎the construction of affine frames for $L^2(G)$ based on a GMS is presented‎.


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