Pseudodifferential equations and a generalized translation operator in non-gaussian infinite-dimensional analysis - Kachanovskii, N. A. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
Pseudodifferential equations of the form $v(D_{χ})y = f$ (where $v$ is a function holomorphic at zero and $D_{χ}$ is a pseudodifferential operator) are studied on spaces of test functions of non-Gaussian infinite-dimensional analysis. The results obtained are applied to construct a generalized translation operator $T^{χ}_y = χ(\langle y, D_{χ}\rangle)$ the already mentioned spaces and to study its properties. In particular, the associativity, the commutativity, and another properties of $T^{χ}_y$ which are analogs of the classical properties of a generalized translation operator.