Dyadic Localization

Part of the Lecture Notes in Mathematics book series (LNM, volume 1767)


This chapter contains a local analysis of Q p(T) based on the dyadic portions. First of all, we give an alternate characterization of Q p in terms of the square mean oscillations over successive bipartitions of arcs in T. Next, we consider the dyadic counterpart Q p d(T) of Q p(T), in particular, we show that fQ p(T) if and only if (almost) all its translates belong to Q d p(T); conversely, functions in Q p(T) may be obtained by averaging translates of functions in Q p(T). Finally, as a natural application of the dyadic model of Q p(T), we present a wavelet expansion theorem of Q p(T).


Wavelet Coefficient Dyadic Interval Haar System Haar Function Complete Orthonormal Basis 
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© Springer-Verlag Berlin Heidelberg 2001

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