Frame characterizations of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type and their applications.
Frame functions and completeness of inner product spaces
Frames associated with expansive matrix dilations.
We construct wavelet-type frames associated with the expansive matrix dilation on the Anisotropic Triebel-Lizorkin spaces. We also show the a.e. convergence of the frame expansion which includes multi-wavelet expansion as a special case.
Frames for Fréchet spaces
From Continous to Discrete Weyl-Heisenberg Frames Through Sampling.
From the Original Framer to Present-Day Time-Frequency and Time-Scale Frames.
Function spaces on the snowflake
We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0,3]. We compare these spaces and characterize them in terms of Daubechies wavelets.