Analytic Representation of Generalized Tempered Distributions of Exponential Growth by Wavelets

Abstract

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.

Multiresolution Expansion and Approximation Order of Generalized Tempered Distributions

“…In the meantime, the tempered distributions of polynomial growth were extended to tempered distributions of | | -growth, K 1 (R), in [5,6] and | | -growth, K (R), in [7,8] or -growth, K (R), in [9,10], where the function ( ) grows faster than any linear functions as | | . We have considered the analytic representation of tempered distributions of -growth with restricted order, K (R), by wavelets [11]. Also, we have shown that the multiresolution expansions of K (R) converges pointwise to the value of the distribution where it exists [12].…”