IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

On the construction of bases and frames for spaces of distributions


A 2008 Preprint by G. Kyriazis and P. Petrushev

  • 2008:07
  • We introduce a new method for constructing bases and frames for general distribution spaces and employ it to the construction of bases for modulation spaces on R^n and frames for Triebel-Lizorkin and Besov spaces on the sphere. Conceptually, our scheme allows the freedom to prescribe the nature, form, or some properties of the constructed basis or frame elements. For instance, they can be linear combinations of a small fixed number of shifts and dilates of any sufficiently smooth and rapidly decaying function. On the sphere, our frame elements consist of smooth functions supported on small shrinking caps.

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