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Advances in Analysis
AAN > Volume 3, Number 1, January 2018

On Reproducing Kernel and Applications

Download PDF  (471 KB)PP. 11-22,  Pub. Date:June 1, 2017


Author(s)
José Claudinei Ferreira, Estela Costa Ferreira
Affiliation(s)
Institute of Exact Sciences, Federal University of Alfenas, Alfenas, Brazil;
Institute of Exact Sciences, Federal University of Alfenas, Alfenas, Brazil
Abstract
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.
Keywords
Positive definite kernel, reproducing kernel, approximation, denseness.
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