Gaussian decompositions in function spaces

by    H. Triebel

Preprint series: 98-18, Analysis

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

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
46F05 Topological linear spaces of test functions, distributions and ultradistributions, See also {46E10, 46E35}

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 $q$.

Keywords: function spaces, wavelets, atomic decompositions

Upload: 1999-01-28

Update: 1999-01-28

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