Wavelets Adapted to Compact Domains in Reproducing Kernel Hilbert Spaces

Reproducing kernel Hilbert spaces and wavelets are both mathematical tools used in system identification and approximation. Reproducing kernel Hilbert spaces are function spaces possessing special characteristics that facilitate the search for solutions to norm minimization problems [3]. As such, they are of interest in a variety of areas including Machine Learning [11]. Wavelets are another modeling tool used for function approximation and analysis. They are desirable due to their multiscale feature, localization in time and frequency, and fast decomposition / reconstruction algorithms. In this work we merge wavelets adapted to compact domains [10] with reproducing kernel Hilbert spaces following the construction developed by R. Opfer [6]. We provide results for the representation, multiscale nature, and decomposition / reconstruction algorithms for approximations arising from the multiscale reproducing kernel Hilbert spaces. Mathematics Subject Classification: 65T60