Series Expansions of Solutions of Differential-Difference Parabolic Equations

Abstract: The Cauchy problem for parabolic differential-difference equations with operators that are sums of differential operators and translation operators and with operators that are their superpositions is investigated. Expansions of solutions of the indicated problem into function series are constructed. The domains of convergence (including uniform convergence) of the indicated series are established. © Pleiades Publishing, Ltd. 2025.