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Loewy’s Results for Ordinary Differential Equations

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Abstract

The idea of factoring an ordinary differential operator, or the corresponding linear ordinary differential equation (ode), into components of lower order originated from the analogous problem for algebraic polynomials. In the latter case, it is the first step when the solutions of the corresponding algebraic equation are to be determined. It turns out that a similar strategy is the key for understanding the structure of the solution space of a linear ode. Good introductions into the subject are the books by Ince [29] or Kamke [32, 34], and the book by van der Put and Singer [71].

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Schwarz, F. (2012). Loewy’s Results for Ordinary Differential Equations. In: Loewy Decomposition of Linear Differential Equations. Texts & Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1286-1_1

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  • DOI: https://doi.org/10.1007/978-3-7091-1286-1_1

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