Distributions Convolution Equa (Hardcover)

The authors apply the results of many years of their own original research to a systematic presentation of the theory of distributions. The first part of their monograph is devoted to the Cauchy problem. The authors show that Petrovskii's classic theory of the correctness of the Cauchy problem for general differential operators with constant coefficients is naturally embedded in a theory of the solvability of convolution equations in certain spaces of distributions. The second part deals with the Wiener-Hopf equation and related topics in the theory of boundary value problems for convolution equations. Here, as in the case of the Cauchy problem, the main technical element is an exact description of certain spaces of convolutes (Wiener-Hopf convolutes).;To make their work more accessible to readers new to this field, the authors restrict initial treatment of problems to the half-line and formulate only principal results, in their simplest form. Special results and possible generalizations are presented as problems and exercises. For this reason this work is recommended not only for experts in the field of partial differential equations, but also for senior under-graduate and graduate students less familiar with this area.