Stability of Nearly Optimal Decompositions in Fourier Analysis

Аннотация

We consider the existence problem for near-minimizers for the distance functional (or E-functional in the interpolation terminology) that are stable under the action of certain operators. In particular, stable near-minimizers for the couple (L¹, L^p) are shown to exist when the operator is the projection to wavelets and these wavelets satisfy only some weak decay conditions at infinity.