Generalized Jordan Sets in the Theory of Singular Partial Differential-Operator Equations

We apply the generalized Jordan sets techniques to reduce partial differential-operator equations with the Fredholm operator in the main expression to regular problems. In addition this techniques has been exploited to prove a theorem of existence and uniqueness of a singular initial problem, as well as to construct the left and right regularizators of singular operators in Banach spaces and to construct fundamental operators in the theory of generalized solutions of singular equations. Introduction Let x = (t, x) be a point in the space R, x = (x1, . . . , xm), D = (Dt, Dx1 , . . . , Dxm), α = (α0, . . . , αm), | α |= α0 + α1 + · · ·αm, where αi are integer non-negative indexes, D α = ∂ ∂tα0 . . . ∂xm m . We also suppose that Bα : Dα ⊂ E1 → E2 are closed linear operators with dense domains in E1, x ∈ Ω, where Ω ⊂ R , | t |≤ T, E1, E2 are Banach spaces. Let us consider the following operator L(D) = ∑