Some equations with pseudodifferential operators in infinite-dimensional space (Q1067188)

Some spaces of generalized measures and of distributions \(\Phi\) (H) connected with two classes of pseudo differential operators \(A^*(D)\), the symbol of which depends on two arguments \((x_ 1,x_ 2)\in H_ 1\times H_ 2\) \((H_ 1\) and \(H_ 2\) are Hilbert spaces). The operators \(A^*(D)\) generate isomorphic maps in these spaces. The class of operators studied in the paper contains all the differential operators with constant coefficients and also some differential operators with variable coefficients of special kind. The results of the paper made possible to prove the existence and uniqueness of the solution \(f:[0,+\infty [\to \Phi (H)\) of the Cauchy problem for the evolution equation \(f'(t)=A(x,D)f(t)+u\), \(f(0)=f_ 0\), \((u,f_ 0\in \Phi (H))\).