Wavelets adapted to compact domains in reproducing kernel Hilbert spaces

Reproducing kernel Hilbert spaces and wavelets are both mathemat-ical tools used in system identication and approximation. Reproducingkernel Hilbert spaces are function spaces possessing special characteris-tics that facilitate the search for solutions to norm minimization prob-lems [3]. As such, they are of interest in a variety of areas includingMachine Learning [11]. Wavelets are another modeling tool used forfunction approximation and analysis. They are desirable due to theirmultiscale feature, localization in time and frequency, and fast decom-position / reconstruction algorithms. In this work we merge waveletsadapted to compact domains [10] with reproducing kernel Hilbert spacesfollowing the construction developed by R. Opfer [6]. We provide re-sults for the representation, multiscale nature, and decomposition / reconstruction algorithms for approximations arising from the multiscale reproducing kernel Hilbert spaces.