Summary of Research Accomplishments
نویسنده
چکیده
1. Wavelets. One of my early accomplishments was the construction of wavelets on hyper-surfaces, extending the two-dimensional work in Coifman, Jones, Semmes (J. of Amer. Math. Soc., 1989), in a desirable fashion. This answered a question raised by G. David (Springer LNM, 1991, p. 75) and was used to provide a new proof of the fundamental result of Coifman, McIntosh, Meyer (Annals of Math., 1982) regarding the L2-boundedness of the Cauchy operator on Lipschitz surfaces. These results have been published in my Springer-Verlag LNM, 1994 book (where “Clifford wavelet” were first introduced). The approach I developed is rather flexible and has been subsequently adapted to other cases of interest by several authors (cf., e.g., Girardi and Sweldens J. Fourier Anal. Appl., 1997, where certain unbalanced Haar-like wavelets that form an unconditional basis for Lp are referred to as “Mitrea wavelets”). The aforementioned book also contains several T (b)-theorems in the context of Clifford algebras, proved via wavelet analysis.
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تاریخ انتشار 2003