Abstract
This paper investigates some properties of multi-scale kernels, mainly those which are related to their native spaces and make the corresponding integral operators well defined in the L p context. In the case p = 2 , we derive results related to the range of the operators, alternative representations, computation of their norms, basic spectral analysis and isolated properties involving the native spaces of the kernels. Even being not compact, the integral operators possess interesting properties which are peculiar to compact operators.
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