Pseudo-Differential Operators of Volterra Type on Spaces of Ultra Distributions and Parabolic Mixed Problems
M. Krishna Murthy · Birkhäuser Boston eBooks · 1989
The calculus of classical pseudo-differential operators has been used in a fundamental way in the study of boudary value problems associated to (systems) of elliptic differential and pseudo-differential operators. This calculus was used by Hörmander in [7] to construct parametrices for the elliptic operators, using which the boundary value problem is reduced to a system of pseudo-differential operators on the boundary. In order to treat the boundary value problems for parabolic operators in bounded cylindrical domains Piriou introduced in [15] and [16] a class of operators which called pseudo-differential operators of Volterra type. The basic idea consists in developping a calculus of an appropriate class of anisotropic pseudo-differential operators as in an earlier note of Hunt and Piriou [8]. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.