Dispersion relations for the multivelocity acoustic Peierls equations and some properties of the scalar acoustic Peierls potential. I

Under consideration are the questions of mathematical justification and development of a diffusive-wave model for sound propagation in a homogeneous Maxwellian gas. The following results are obtained: The symbols of the convolution kernels of multivelocity acoustic Peierls equations are calculated by means of special functions, and dispersion relations are written down for them. The absence of three-dimensional real leaves of solutions is established for a scalar dispersion relation. The asymptotics at infinity is calculated for a scalar monochromatic Peierls potential, and uniqueness is established for a solution to the inverse potential problem for it in the class of all compactly-supported distributions. The article is split into two parts and comprises three sections. Part I, comprising § 1, contains the statements of all main results of the article.