On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms

Abstract

In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of Lp→(Rd) are also given.

Keywords

• mixed-norm Lebesgue space
• mixed-norm Wiener amalgam space
• shift-invariant subspace
• sampling theory
• stability theory
• iterative algorithm