Let K (R) be the generalized tempered distributions of-growth with restricted order N 0 , where the function () grows faster than any linear functions as | |. We show the convergence of multiresolution expansions of K (R) in the test function space K (R) of K (R). In addition, we show that the kernel of an integral operator K (R) K (R) provides approximation order in K (R) in the context of shift-invariant spaces.

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Abstract. The analytic representation of the generalized tempered distributions of e MðkxÞ -growth with restricted order, K r0 M ðRÞ, is given in terms of series of analytic wavelets. These series converge uniformly on compact subsets of the upper and lower half planes.