On the reduction of resolvent integral operators upon construction of solutions of linear viscoelasticity problems (Q2754669)

Solution of problems of linear viscoelasticity on the basis of Boltzmann-Volterra principle and the method of operator continued fractions at some stage requires expanding rational functions of Volterra resolvent integral operators. For these the degrees of operators usually are equal to or less than two. Often, parts of operators in the numerator and denominator have the same parameters. In the paper it is proved that, by expanding a rational function, the operators with coinciding parameters are abbreviated by cancellation irrespective of initial coefficients. This property of resolvent operators allows one to put coefficients of the corresponding operators equal to zero without calculating them.