Multiresolution Expansion and Approximation Order of Generalized Tempered Distributions

Abstract EN

Let ?Mr′(ℝ) be the generalized tempered distributions of eM(x)-growth with restricted order r∈ℕ0, where the function M(x) grows faster than any linear functions as |x|→∞.

We show the convergence of multiresolution expansions of ?Mr′(ℝ) in the test function space ?Mr(ℝ) of ?Mr′(ℝ).

In addition, we show that the kernel of an integral operator K:?Mr′(ℝ)→?Mr′(ℝ) provides approximation order in ?Mr′(ℝ) in the context of shift-invariant spaces.