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Properties of Jost and dual Jost solutions of the heat equation, $\Phi(x,k)$and $\Psi(x,k)$, in the case of a pure solitonic potential are studied indetail. We describe their analytical properties on the spectral parameter $k$and their asymptotic behavior on the $x$-plane and we show that the values of$e^{-qx}\Phi(x,k)$ and the residua of $e^{qx}\Psi(x,k)$ at special discretevalues of $k$ are bounded functions of $x$ in a polygonal region of the$q$-plane. Correspondingly, we deduce that the extended version $L(q)$ of theheat operator with a pure solitonic potential has left and right annihilatorsfor $q$ belonging to these polygonal regions.

Heat operator with pure soliton potential: properties of Jost and dual Jost solutions