Parabolic pseudodifferential equations, hypersingular integrals, and Markov processes

A fundamental solution of the Cauchy problem is constructed and investigated for the equation $\frac{\partial u}{\partial t}+Au=f$, where $A$ is a pseudodifferential operator whose symbol is a sum of homogeneous functions. The results are used for an analytic construction of discontinuous Markov processes.
Bibliography: 42 titles.