Mathematical Sciences: Asymptotically Holomorphic Functions and Certain of Their Applications

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In this project the principal investigators will continue their study of what are called "asymptotically holomorphic" (AH) functions. AH functions are smooth functions that share many of the uniqueness properties of true holomorphic functions. Specifically the principal investigators will establish certain unifying results based upon a general Phragmen-Lindelof principle for AH functions and upon the idea of a generalized Fourier- Carleman transform. Asymptotically holomorphic (AH) functions are a recent generalization of holomorphic (i.e., analytic) functions that arise naturally in connection with problems in approximation theory, harmonic analysis and dynamical systems theory. In this project the principal investigators will extend our knowledge of AH functions and at the same time, examine further applications of these functions in the three areas just mentioned. The researchers are working currently on a monograph that will make these important ideas available to a wide audience. ***//