Linear operators generated by a countable number of quasi-differential expressions.

*(English)*Zbl 1049.47043The 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 \(\mathbb R\).

Reviewer: Constantin Corduneanu (Arlington)

##### 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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\textit{R. R. Ashurov} and \textit{W. N. Everitt}, Appl. Anal. 81, No. 6, 1405--1425 (2002; Zbl 1049.47043)

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##### References:

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