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Factorization of quasi-differential operators


Authors: W. N. Everitt, James S. Muldowney and Neeza Thandi
Journal: Proc. Amer. Math. Soc. 113 (1991), 93-98
MSC: Primary 34L99; Secondary 34A30, 47E05
DOI: https://doi.org/10.1090/S0002-9939-1991-1045592-1
MathSciNet review: 1045592
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Abstract: A quasi-differential generalization of operators of the form $ {l_n}u = {u^{(n)}} + {p_1}{u^{(n - 1)}} + \cdots + {p_n}u$ is considered. This type of generalization was first formulated by M. Bôcher (1913). A result of A. Zettl (1971) giving a necessary and sufficient condition that a differential operator $ {l_n}$ be factorable into a product of lower order differential operators is extended to quasi-differential expressions.


References [Enhancements On Off] (What's this?)

  • [1] M. Bôcher, Applications and generalizations of the concept of adjoint systems, Trans. Amer. Math. Soc. 14 (1913), 403-420. MR 1500954
  • [2] -, Leçons sur les méthodes de Sturm dans la théorie des equations differentielles linéaires et leurs dévelloppements modernes, Gauthier-Villars, Paris, 1917.
  • [3] W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 20, Springer-Verlag, New York, 1971. MR 0460785 (57:778)
  • [4] G. J. Etgen, G. D. Jones, and W. E. Taylor, Jr., On the factorizations of ordinary linear differential operators, Trans. Amer. Math. Soc. 297 (1986), 717-728. MR 854095 (87k:34049)
  • [5] W. N. Everitt, Linear control theory and quasi-differential equations, J. Applied Math. Phys. 38 (1987), 193-203. MR 885683 (89c:93010)
  • [6] F. R. Gantmacher, The theory of matrices, vol. I, Chelsea, New York, 1960.
  • [7] P. Hartman, Ordinary differential equations, Wiley, New York, 1964. MR 0171038 (30:1270)
  • [8] J. S. Muldowney, On an inequality of Čaplygin and Pólya, Proc. Roy. Irish Acad. Sect. A 76 (1976), 85-99. MR 0409943 (53:13695)
  • [9] -, Markov systems of vector-valued functions and disconjugacy, J. Approx. Theory 59 (1989), 53-71. MR 1033893 (91i:34103)
  • [10] Z. Nehari, Disconjugate linear differential operators, Trans. Amer. Math. Soc. 129 (1967), 500-516. MR 0219781 (36:2860)
  • [11] G Pólya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 29 (1922), 312-324. MR 1501228
  • [12] A. Zettl, Factorization of differential operators, Proc. Amer. Math. Soc. 27 (1971), 425-426. MR 0273085 (42:7966)
  • [13] -, Formally self-adjoint quasi-differential operators, Rocky Mountain J. Math. 5 (1975), 453-474. MR 0379976 (52:880)

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DOI: https://doi.org/10.1090/S0002-9939-1991-1045592-1
Article copyright: © Copyright 1991 American Mathematical Society

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