Sampling theorem on shift invariant subspaces in mixed Lebesgue spaces

Abstract

Sampling theorem is the theoretical basis of modern communication system, and is also one of the most powerful basic tools in signal processing and image processing. In this paper, we give sampling theorem on shift invariant subspaces in mixed Lebesgue spaces L^p,q(ℝ^d+1). When the sampling density is large enough, this sampling theorem can reconstruct exactly the signals in shift invariant subspaces. Our results improve the result in [6].

Subject Classification:

• (2010) 94A20
• 94A12
• 42C15
• 41A58

Keywords:

• Sampling theorem
• Mixed Lebesgue spaces
• Shift invariant subspaces