2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160930We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between $L_2$-small ball asymptotics of the transformed function and of the original one. Also the explicit Karhunen -- Loéve expansion is obtained for a proper class of Gaussian processes.Probability60G15text