Search for Lepton Number and Flavor violations in K decays at the NA62 experiment

The work presented in this thesis has been carried out using the data collected at the NA62 experiment at CERN. The study aims at contributing to new physics searches looking for Lepton Number and Flavor violations in charged kaon decays, focusing on the $K^+ \to \pi^+ \mu^+ e^- , K^+ \to \pi^+ \mu^- e^+ $ and $K^+ \to \pi^- \mu^+ e^+ $ channels. The results have been obtained analyzing $17 \times 10^{10}$ kaon decays from 2016 and 2017 data taking. The estimated Single Event Sensitivity and the preliminary results obtained with the Rolke-Lopetz method show improvements on the present experimental limits in the $K^+ \to \pi^+ \mu^- e^+ $ and $ K^+ \to \pi^- \mu^+ e^+ $ channels, while for $K^+ \to \pi^+ \mu^+ e^- $ more statistics is needed.