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Positive definite or reproducing kernel are common topics in recent branches of mathematics. In this paper we brief review some facts about this subject and prove some technical results related to convergence, representations by using integral operators, embedding properties, denseness and strict positive definiteness. As an application point of view, we close the paper choosing a special basis to approximate solutions to Volterra integral equations.
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Ferreira et al. (2018) studied this question.
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