THIS TALK WILL BE RESCHEDULED SHORTLY!
This talk concerns functions of several variables satisfying the mixed Hölder condition. I will review favorable results for such functions as regards sampling, compression, and approximation -- in particular, the sparse grid construction of Smolyak, and the tensor wavelet approximation of Strömberg. I will demonstrate that these can be adapted to tree metrics, a natural setting for many data analysis problems. I will also introduce Besov-type norms for products of tree metrics and show how these induce a new family of Calderón-Zygmund decompositions. I will conclude by presenting applications to the organization of multidimensional databases. This is joint work with Jerrod Ankenman and Ronald Coifman.