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Linear operators generated by a countable number of quasi-differential expressions. (English) Zbl 1049.47043
The aim of this paper is the extension of the theory of linear ordinary quasi-differential operators (on spaces of locally integrable functions in the sense of Lebesgue) on a single interval of the real axis, to the case of operators when a finite number or a countable family of intervals is involved. The underlying spaces are not anymore Banach spaces, but locally convex linear topological spaces whose topology is defined by a countable family of seminorms. The quasi-differential operators are with variable coefficients. Interesting properties are obtained, using rather complex tools. Since any open set on \(\mathbb R\) can be represented as the union of a countable family of disjoint intervals, it means that the results are applicable whenever the coefficients of the quasi-differential operators are defined on an open set of \(\mathbb R\).

MSC:
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
34A30 Linear ordinary differential equations and systems, general
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46A03 General theory of locally convex spaces
34G10 Linear differential equations in abstract spaces
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