On the Construction of Frames for Triebel-lizorkin and Besov Spaces
نویسندگان
چکیده
We present a general method for construction of frames {ψI}I∈D for Triebel-Lizorkin and Besov spaces, whose nature can be prescribed. In particular, our method allows for constructing frames consisting of rational functions or more general functions which are linear combinations of a fixed (small) number of shifts and dilates of a single smooth and rapidly decaying function θ such as the Gaussian θ(x) = exp(−|x|2). We also study the boundedness and invertibility of the frame operator Sf = ∑ I∈D〈f, ψI〉ψI on Triebel-Lizorkin and Besov spaces and give necessary and sufficient conditions for the dual system {S−1ψ}I∈D to be a frame as well.
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