Unified approach and technique to performance of Mellin convolution and related integral transforms in relaxation experiments (Q1374151)

The paper contains the study of linear viscoelastic behaviour of solid materials. Generalized integral transforms in the form of the convolution Mellin transform of direct and inverse type are used for analysing the problem. A method is developed for performing integral transforms with kernels depending on the division or product of arguments based on digital filtering of the logarithmically transformed measurement data. A method of regularization is proposed for ill-conditioned problems where the sampling rate is used as a regularization parameter. It is shown that filters with shifted impulse responses can be used for expanding the range of the output function. Examples of performing the Heaviside-Carson sine transform and an inherently ill-conditioned inversion for the determination of the relaxation spectrum are represented.