Advances in Analysis

Download PDF (549.4 KB) PP. 11 - 22 Pub. Date: January 4, 2018

DOI: 10.22606/aan.2018.31002

• José Claudinei Ferreira^*
  Institute of Exact Sciences, Federal University of Alfenas, Alfenas, Brazil
• Estela Costa Ferreira
  
  Institute of Exact Sciences, Federal University of Alfenas, Alfenas, Brazil

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.

Positive definite kernel, reproducing kernel, approximation, denseness.

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