IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Decomposition of spaces of distributions induced by Hermite expansions

A 2007 Preprint by P. Petrushev and Y. Xu

  • 2007:06
  • Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $R^d$ induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite Triebel-Lizorkin and Besov spaces are, in general, different from the respective classical spaces.

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