On the construction of frames for spaces of distributions

We introduce a new method for constructing frames for general distribution spaces and employ it to the construction of 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 frame elements. For instance, our frame elements on the sphere consist of smooth functions supported on small shrinking caps. © 2009 Elsevier Inc. All rights reserved.