On some properties and limiting values of resolvent integral operators of viscoelasticity (Q2754787)

Resolvent integral Volterra operators of the first kind are used in solutions of problems of linear viscoelasticity. Making use of relationships defining them and formulae of their inversion and multiplication, the author proves the boundedness in time and monotonicity with respect to parameter of viscoelastic operators, and examines their limits as \(t\to\infty\). The limiting transition as \(t\to\infty\) in the operator continued fraction is done. Signs of resolvent operators in dependence on signs of their parameters are studied. Relationships between operators with complex conjugate parameters are derived.