Gaussian decompositions in function spaces

Preprint series: 98-18, Analysis

The paper is published: Result. Math., 34, 174-184, 1998

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems
Abstract: We introduce Gausslets $e^{- \frac{|x|^2}{2}} P(x)$, where $P(x)$ are distinguished polynomials in ${\Bbb{R}}^n$.
Combined with dilations $x \mapsto 2^\nu x$, where $\nu\in {\Bbb{N}}_0$, and translations $x \mapsto x + m$, where $m \in {\Bbb{Z}}^n$,
one obtains frames in the function spaces $B^s_{pq}({\Bbb{R}}^n)$ and $F^s_{pq} ({\Bbb{R}}^n)$ for all possible parameters $s, p,$ and $q$.