Multiresolution Expansions of Distributions: Pointwise Convergence and Quasiasymptotic Behavior
In several variables, we prove the pointwise convergence of multiresolution expansions to the distributional point values of tempered distributions and distributions of superexponential growth. The article extends and improves earlier results by G.G. Walter and B.K. Sohn and D.H. Pahk that were shown in one variable. We also provide characterizations of the quasiasymptotic behavior of distributions at finite points and discuss connections with ?-density points of measures.
quasiasymptotics pointwise convergence of multiresolution expansions tempered distributions distributions of superexponential growth ?-density points multiresolution analysis (mra) regularly varying functions asymptotic behavior of generalized functions 42c40 46f12 26a12 41a60 46f10