Dr. Theofanis Sapatinas (University of Cyprus and UCSB)

Title: Functional Deconvolution in a Periodic Setting: Continuous and Discrete Models

Abstract: We present an extension of deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation. In the case when it is observed at a finite number of distinct points, the proposed functional deconvolution model can also be viewed as a multichannel deconvolution model. We present adaptive minimax wavelet block-thresholding estimators over a wide range of Besov spaces and investigate when the availability of continuous data gives advantages over observations at the asymptotically large number of points. As an illustration, we discuss particular examples for both continuous and discrete settings. Some recent developments are also briefly discussed.