The Approximations for Degenerate $C_0$-semigroup

The results from the theory of Sobolev type equations have been actively used to measure the dynamically distorted signals recently. The formulas obtained for relatively $p$-radial case of Sobolev type equations are used for the numerical solution of such problems. Hille–Widder–Post approximations for the operators of strongly continuous resolving semigroup for homogeneous equations are considered in the article. The authors show that a simpler formula can be used as approximations of operators of a resolving semigroup.
The article consists of introduction and two parts. The information regarding the relative resolutions and theories of relatively $p$-radial operators are given in the first part. The approximation formulas are covered in the second part.