The asymptotics of some evolution equations

We consider the contributions to the asymptotics of the function exp (T), t± , caused by the spectral singularity of a nonselfadjoint Sturm-Liouville operator T in the space L²(0, ). The potential is assumed to decrease like a power of the variable, and the element belongs to the domain of definition of both the operator T and a certain extension of it to increasing functions.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 75–85.