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We study the spectral functions, the poles and their trajectories forincreasing $N_{c}$ of the vector kaon state $K^{\ast}(892),$ characterized by$I(J^{P})=\frac{1}{2}(1^{-})$, and of the scalar kaons $K_{0}^{\ast}(800)$ and$K_{0}^{\ast}(1430),$ characterized by $I(J^{P})=\frac{1}{2}(0^{+})$. To thisend, we use relativistic QFT's Lagrangians with both derivative andnon-derivative terms. In the vector kaonic sector the spectral function is wellapproximated by a Breit-Wigner function: there is one single peak and,correspondingly, a single pole in the complex plane. On the contrary, in thescalar sector, although the Lagrangian contains only one scalar kaonic field,we find two poles, one corresponding to a standard quark-antiquark,,seed\textquotedblright\ state $K_{0}^{\ast}(1430),$ and one to a\textquotedblleft companion\textquotedblright\ dynamically generate pole$K_{0}^{\ast}(800)$. The latter does not correspond to any peak in the scalarkaonic spectral function, but only to an enhancement in the low-energy regime.

Large-$N_{c}$ pole trajectories of the vector kaon $K^{\ast}(892) $ and of the scalar kaons $K_{0}^{\ast}(800)$ and $K_{0}^{\ast}(1430)$