Average sampling in mixed shift-invariant subspaces with generators in
hybrid-norm spaces
Abstract
This paper mainly studies the average sampling and reconstruction in
shift-invariant subspaces of mixed Lebesgue spaces
$L^{p,q}(\mathbb{R}^{d+1})$, under the
condition that the generator $\varphi$ of the
shift-invariant subspace belongs to a hybrid-norm space of mixed form,
which is weaker than the usual assumption of Wiener amalgam space and
allows to control the orders $p,q$. First, the sampling stability for
two kinds of average sampling functionals are established. Then, we give
the corresponding iterative approximation projection algorithms with
exponential convergence for recovering the time-varying shift-invariant
signals from the average samples.